diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5e95d096c592112060111541576ef409a463a586..bb744379f80a961039b35ef009750450a076c81b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,7 @@ Differences Between DuMu<sup>x</sup> 3.9 and DuMu<sup>x</sup> 3.8
 - __Darcy-Brinkman Freeflow__: There is no a convenience function to add a Brinkman term to turn the Navier-Stokes model into the Darcy-Brinkman model. With this, a single domain can contain both free flow and flow through a porous medium.
 The term is added as a source term in the problem using the new helper function `addBrinkmanTerm`.
 The function uses new spatial parameter interface implemented in the new `BrinkmanSpatialParams` class (`dumux/freeflow/spatialparams.hh`). The helper function can deal with isotropic and anisotropic permeabilites.
+- __Facet-Coupling__: Fixed the handling of duplicate degrees of freedom in the box facet-coupling model in the corner case that an internal fracture turns into a boundary fracture (see [merge request 3748](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/merge_requests/3748) for images).
 
 ### Immediate interface changes not allowing/requiring a deprecation period:
 
diff --git a/dumux/multidomain/facet/vertexmapper.hh b/dumux/multidomain/facet/vertexmapper.hh
index 4d7aca243ecbc3f4fe707c79072fd3c1f489ae64..82cb88f3d542b751559b3382f79aa5f794ef3224 100644
--- a/dumux/multidomain/facet/vertexmapper.hh
+++ b/dumux/multidomain/facet/vertexmapper.hh
@@ -77,21 +77,17 @@ public:
                                                              dim ) ] = true;
         }
 
-        // for now, set all markers to true for vertices on codim one grid
-        for (const auto& vertex : vertices(codimOneGridView))
-            vertexMarkers[codimOneGridAdapter.bulkGridVertexIndex(vertex)] = true;
-
-        // unmark where necessary
+        // mark all vertices on the lower-dimensional grid to be enriched (except immersed boundaries)
+        std::vector<typename GridView::IndexSet::IndexType> vertexIndicesStorage;
         for (const auto& codimOneElement : elements(codimOneGridView))
         {
-            // if a codimension one element has less than two embedments  we do not need to enrich
-            if (codimOneGridAdapter.numEmbedments(codimOneElement) < 2)
+            // if a codimension one element has 2 or more embedments, we need to enrich
+            if (codimOneGridAdapter.numEmbedments(codimOneElement) >= 2)
+            {
                 for (int i = 0; i < codimOneElement.subEntities(dim-1); ++i)
-                    vertexMarkers[ codimOneGridAdapter.bulkGridVertexIndex(codimOneElement.template subEntity<dim-1>(i)) ] = false;
+                    vertexMarkers[ codimOneGridAdapter.bulkGridVertexIndex(codimOneElement.template subEntity<dim-1>(i)) ] = true;
 
-            // otherwise, we check for immersed boundaries where we also must not enrich
-            else
-            {
+                // however, we have to exclude immersed boundaries
                 const auto refElem = referenceElement(codimOneElement);
                 for (const auto& intersection : intersections(codimOneGridView, codimOneElement))
                 {
@@ -99,18 +95,18 @@ public:
                     if (!intersection.boundary())
                         continue;
 
-                    // obtain all grid indices of the intersection corners
+                    // obtain all bulk grid indices of the lower-dimensional intersection corners
                     const auto numCorners = intersection.geometry().corners();
-                    std::vector<typename GridView::IndexSet::IndexType> vertexIndices(numCorners);
+                    vertexIndicesStorage.resize(numCorners);
                     for (int i = 0; i < numCorners; ++i)
                     {
                         const auto vIdxLocal = refElem.subEntity(intersection.indexInInside(), 1, i, dim-1);
-                        vertexIndices[i] = codimOneGridAdapter.bulkGridVertexIndex( codimOneElement.template subEntity<dim-1>(vIdxLocal) );
+                        vertexIndicesStorage[i] = codimOneGridAdapter.bulkGridVertexIndex( codimOneElement.template subEntity<dim-1>(vIdxLocal) );
                     }
 
                     // if any of the vertices is on an immersed boundary, we must not enrich any of them
-                    if (std::any_of(vertexIndices.begin(), vertexIndices.end(), [&isOnBoundary] (auto idx) { return !isOnBoundary[idx]; }))
-                        std::for_each(vertexIndices.begin(), vertexIndices.end(), [&vertexMarkers] (auto idx) { vertexMarkers[idx] = false; });
+                    if (std::any_of(vertexIndicesStorage.begin(), vertexIndicesStorage.end(), [&isOnBoundary] (auto idx) { return !isOnBoundary[idx]; }))
+                        std::for_each(vertexIndicesStorage.begin(), vertexIndicesStorage.end(), [&vertexMarkers] (auto idx) { vertexMarkers[idx] = false; });
                 }
             }
         }
diff --git a/test/multidomain/facet/1p_1p/CMakeLists.txt b/test/multidomain/facet/1p_1p/CMakeLists.txt
index c9373435f8b1745b6caad4988ad2ecd92af07766..c90c1216471c44a865e819969c906d493d08968d 100644
--- a/test/multidomain/facet/1p_1p/CMakeLists.txt
+++ b/test/multidomain/facet/1p_1p/CMakeLists.txt
@@ -2,6 +2,7 @@
 # SPDX-License-Identifier: GPL-3.0-or-later
 
 add_subdirectory(analytical)
+add_subdirectory(box_dof_enrichment)
 add_subdirectory(gravity)
 add_subdirectory(linearprofile)
 add_subdirectory(threedomain)
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/CMakeLists.txt b/test/multidomain/facet/1p_1p/box_dof_enrichment/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eebfce386f4837118050e6e99745f6f0dc594c01
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/CMakeLists.txt
@@ -0,0 +1,39 @@
+# SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+# SPDX-License-Identifier: GPL-3.0-or-later
+
+# These tests test the behaviour of the box-facet-coupling model in the case that a fracture ends
+# at the boundary, or extends beyond the boundary. In both cases, the dofs at the boundary of the
+# bulk domain have to be duplicated in order to account for possible pressure jumps. The tests use
+# a very low fracture permeability, and we use the same bulk reference solution to test against.
+
+dune_symlink_to_source_files(FILES "grids" "params.input")
+
+add_executable(test_md_facet_1p1p_box_dof_enrichment EXCLUDE_FROM_ALL main.cc)
+
+dumux_add_test(NAME test_md_facet_1p1p_box_dof_enrichment_extended_fracture
+               TARGET test_md_facet_1p1p_box_dof_enrichment
+               LABELS multidomain multidomain_facet 1p
+               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+               COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+               CMD_ARGS  --script fuzzy
+                         --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_dof_enrichment_extended_fracture_bulk-reference.vtu
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_dof_enrichment_extended_fracture_bulk-00001.vtu
+                                 ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_dof_enrichment_extended_fracture_lowdim-reference.vtp
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_dof_enrichment_extended_fracture_lowdim-00001.vtp
+                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_box_dof_enrichment params.input \
+                                                                            -Grid.File grids/extended_fracture.msh \
+                                                                            -Vtk.OutputName test_md_facet_1p1p_dof_enrichment_extended_fracture")
+
+dumux_add_test(NAME test_md_facet_1p1p_box_dof_enrichment_short_fracture
+               TARGET test_md_facet_1p1p_box_dof_enrichment
+               LABELS multidomain multidomain_facet 1p
+               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+               COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+               CMD_ARGS  --script fuzzy
+                         --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_dof_enrichment_extended_fracture_bulk-reference.vtu
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_dof_enrichment_short_fracture_bulk-00001.vtu
+                                 ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_dof_enrichment_short_fracture_lowdim-reference.vtp
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_dof_enrichment_short_fracture_lowdim-00001.vtp
+                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_box_dof_enrichment params.input \
+                                                                            -Grid.File grids/short_fracture.msh \
+                                                                            -Vtk.OutputName test_md_facet_1p1p_dof_enrichment_short_fracture")
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/extended_fracture.msh b/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/extended_fracture.msh
new file mode 100644
index 0000000000000000000000000000000000000000..b4dacfedf299455eccd1ff791e734b16049f74fe
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/extended_fracture.msh
@@ -0,0 +1,3518 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
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diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/geometry.geo b/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/geometry.geo
new file mode 100644
index 0000000000000000000000000000000000000000..5c982c0390160ca9cb07827cfc025d856813617d
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/geometry.geo
@@ -0,0 +1,46 @@
+// domain measures
+xmax = 1.0;
+ymax = 3.0;
+inlet_size = 0.2;
+mesh_size = 0.05;
+
+Point(0) = {0, 0, 0, mesh_size};
+Point(1) = {xmax, 0, 0, mesh_size};
+
+Point(2) = {0, ymax/2, 0, mesh_size};
+Point(3) = {inlet_size, ymax/2, 0, mesh_size};
+Point(4) = {xmax - inlet_size, ymax/2, 0, mesh_size};
+Point(5) = {xmax, ymax/2, 0, mesh_size};
+
+Point(6) = {inlet_size, ymax, 0, mesh_size};
+Point(7) = {xmax - inlet_size, ymax, 0, mesh_size};
+
+Line(0) = {0, 1};
+Line(1) = {0, 2};
+
+Line(2) = {2, 3};
+Line(3) = {3, 4};
+Line(4) = {4, 5};
+
+Line(5) = {3, 6};
+Line(6) = {4, 7};
+
+Line(7) = {6, 7};
+Line(8) = {1, 5};
+
+Curve Loop(1) = {0, 8, -4, -3, -2, -1};
+Plane Surface(1) = {1};
+
+Curve Loop(2) = {3, 6, -7, -5};
+Plane Surface(2) = {2};
+
+// to not extend the fracture beyond the top-domain boundary,
+// you may use the command-line argument "-setnumber extend_fracture 0"
+DefineConstant[ extend_fracture = 1 ];
+
+Physical Line(1) = {3};
+If (extend_fracture)
+    Physical Line(2) = {2, 4};
+EndIf
+
+Physical Surface(1) = {1, 2};
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/short_fracture.msh b/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/short_fracture.msh
new file mode 100644
index 0000000000000000000000000000000000000000..9459f5325f1ae61c87c5b65f601716771037955a
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/grids/short_fracture.msh
@@ -0,0 +1,3510 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
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+$EndElements
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/main.cc b/test/multidomain/facet/1p_1p/box_dof_enrichment/main.cc
new file mode 100644
index 0000000000000000000000000000000000000000..0f8344272db8ee6d42bf10348db7b6a1eafea493
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/main.cc
@@ -0,0 +1,176 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup FacetTests
+ * \brief Test for the one-phase facet coupling model using the box scheme,
+ *        considering fractures that extend across the boundary.
+ */
+
+#include <config.h>
+
+#include <iostream>
+
+#include <dune/common/parallel/mpihelper.hh>
+
+#include <dumux/common/initialize.hh>
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/dumuxmessage.hh>
+
+#include <dumux/linear/istlsolvers.hh>
+#include <dumux/linear/linearsolvertraits.hh>
+#include <dumux/linear/linearalgebratraits.hh>
+
+#include <dumux/multidomain/newtonsolver.hh>
+#include <dumux/multidomain/fvassembler.hh>
+#include <dumux/multidomain/traits.hh>
+
+#include <dumux/multidomain/facet/gridmanager.hh>
+
+#include <dumux/io/vtkoutputmodule.hh>
+
+#include "properties.hh"
+
+// main program
+int main(int argc, char** argv)
+{
+    using namespace Dumux;
+
+    //////////////////////////////////////////////////////
+    //////////////////////////////////////////////////////
+
+    // maybe initialize MPI and/or multithreading backend
+    Dumux::initialize(argc, argv);
+    const auto& mpiHelper = Dune::MPIHelper::instance();
+
+    // print dumux start message
+    if (mpiHelper.rank() == 0)
+        DumuxMessage::print(/*firstCall=*/true);
+
+    // initialize parameter tree
+    Parameters::init(argc, argv);
+
+    //////////////////////////////////////////////////////
+    // try to create the grids (from the given grid file)
+    //////////////////////////////////////////////////////
+    using BulkProblemTypeTag = Properties::TTag::OnePBulkBox;
+    using LowDimProblemTypeTag = Properties::TTag::OnePLowDimBox;
+    using BulkGrid = GetPropType<BulkProblemTypeTag, Properties::Grid>;
+    using LowDimGrid = GetPropType<LowDimProblemTypeTag, Properties::Grid>;
+
+    using GridManager = FacetCouplingGridManager<BulkGrid, LowDimGrid>;
+    GridManager gridManager;
+    gridManager.init();
+    gridManager.loadBalance();
+
+    ////////////////////////////////////////////////////////////
+    // run stationary, non-linear problem on this grid
+    ////////////////////////////////////////////////////////////
+
+    // we compute on the leaf grid views
+    const auto& bulkGridView = gridManager.template grid<0>().leafGridView();
+    const auto& lowDimGridView = gridManager.template grid<1>().leafGridView();
+
+    // create the finite volume grid geometries
+    using BulkFacetGridAdapter = Dumux::CodimOneGridAdapter<typename GridManager::Embeddings, 0, 1>;
+    using BulkFVGridGeometry = GetPropType<BulkProblemTypeTag, Properties::GridGeometry>;
+    using LowDimFVGridGeometry = GetPropType<LowDimProblemTypeTag, Properties::GridGeometry>;
+    BulkFacetGridAdapter facetGridAdapter(gridManager.getEmbeddings());
+    auto bulkFvGridGeometry = std::make_shared<BulkFVGridGeometry>(bulkGridView, lowDimGridView, facetGridAdapter);
+    auto lowDimFvGridGeometry = std::make_shared<LowDimFVGridGeometry>(lowDimGridView);
+
+    // the coupling mapper
+    using TestTraits = Properties::TestTraits<BulkProblemTypeTag, LowDimProblemTypeTag>;
+    auto couplingMapper = std::make_shared<typename TestTraits::CouplingMapper>();
+    couplingMapper->update(*bulkFvGridGeometry, *lowDimFvGridGeometry, gridManager.getEmbeddings());
+
+    // the coupling manager
+    using CouplingManager = typename TestTraits::CouplingManager;
+    auto couplingManager = std::make_shared<CouplingManager>();
+
+    // the problems (boundary conditions)
+    using BulkProblem = GetPropType<BulkProblemTypeTag, Properties::Problem>;
+    using LowDimProblem = GetPropType<LowDimProblemTypeTag, Properties::Problem>;
+    auto bulkSpatialParams = std::make_shared<typename BulkProblem::SpatialParams>(bulkFvGridGeometry, "Bulk");
+    auto bulkProblem = std::make_shared<BulkProblem>(bulkFvGridGeometry, bulkSpatialParams, couplingManager, "Bulk");
+    auto lowDimSpatialParams = std::make_shared<typename LowDimProblem::SpatialParams>(lowDimFvGridGeometry, "LowDim");
+    auto lowDimProblem = std::make_shared<LowDimProblem>(lowDimFvGridGeometry, lowDimSpatialParams, couplingManager, "LowDim");
+
+    // the solution vector
+    using MDTraits = typename TestTraits::MDTraits;
+    using SolutionVector = typename MDTraits::SolutionVector;
+    SolutionVector x;
+
+    static const auto bulkId = typename MDTraits::template SubDomain<0>::Index();
+    static const auto lowDimId = typename MDTraits::template SubDomain<1>::Index();
+    x[bulkId].resize(bulkFvGridGeometry->numDofs());
+    x[lowDimId].resize(lowDimFvGridGeometry->numDofs());
+    bulkProblem->applyInitialSolution(x[bulkId]);
+    lowDimProblem->applyInitialSolution(x[lowDimId]);
+
+    // initialize coupling manager
+    couplingManager->init(bulkProblem, lowDimProblem, couplingMapper, x);
+
+    // the grid variables
+    using BulkGridVariables = GetPropType<BulkProblemTypeTag, Properties::GridVariables>;
+    using LowDimGridVariables = GetPropType<LowDimProblemTypeTag, Properties::GridVariables>;
+    auto bulkGridVariables = std::make_shared<BulkGridVariables>(bulkProblem, bulkFvGridGeometry);
+    auto lowDimGridVariables = std::make_shared<LowDimGridVariables>(lowDimProblem, lowDimFvGridGeometry);
+    bulkGridVariables->init(x[bulkId]);
+    lowDimGridVariables->init(x[lowDimId]);
+
+    // initialize the vtk output module
+    using BulkSolutionVector = std::decay_t<decltype(x[bulkId])>;
+    using LowDimSolutionVector = std::decay_t<decltype(x[lowDimId])>;
+    VtkOutputModule<BulkGridVariables, BulkSolutionVector> bulkVtkWriter(*bulkGridVariables, x[bulkId], bulkProblem->name(), "Bulk", Dune::VTK::nonconforming);
+    VtkOutputModule<LowDimGridVariables, LowDimSolutionVector> lowDimVtkWriter(*lowDimGridVariables, x[lowDimId], lowDimProblem->name(), "LowDim");
+
+    // Add model specific output fields
+    using BulkIOFields = GetPropType<BulkProblemTypeTag, Properties::IOFields>;
+    using LowIOFields = GetPropType<LowDimProblemTypeTag, Properties::IOFields>;
+    BulkIOFields::initOutputModule(bulkVtkWriter);
+    LowIOFields::initOutputModule(lowDimVtkWriter);
+
+    // write initial solution
+    bulkVtkWriter.write(0.0);
+    lowDimVtkWriter.write(0.0);
+
+    // the assembler
+    using Assembler = MultiDomainFVAssembler<MDTraits, CouplingManager, DiffMethod::numeric, /*implicit?*/true>;
+    auto assembler = std::make_shared<Assembler>( std::make_tuple(bulkProblem, lowDimProblem),
+                                                  std::make_tuple(bulkFvGridGeometry, lowDimFvGridGeometry),
+                                                  std::make_tuple(bulkGridVariables, lowDimGridVariables),
+                                                  couplingManager);
+
+    // the linear solver
+    using LinearSolver = ILUBiCGSTABIstlSolver<SeqLinearSolverTraits, LinearAlgebraTraitsFromAssembler<Assembler>>;
+    auto linearSolver = std::make_shared<LinearSolver>();
+
+    // the non-linear solver
+    using NewtonSolver = Dumux::MultiDomainNewtonSolver<Assembler, LinearSolver, CouplingManager>;
+    auto newtonSolver = std::make_shared<NewtonSolver>(assembler, linearSolver, couplingManager);
+
+    // linearize & solve
+    newtonSolver->solve(x);
+
+    // update grid variables for output
+    bulkGridVariables->update(x[bulkId]);
+    lowDimGridVariables->update(x[lowDimId]);
+
+    // write vtk output
+    bulkVtkWriter.write(1.0);
+    lowDimVtkWriter.write(1.0);
+
+    ////////////////////////////////////////////////////////////
+    // finalize, print dumux message to say goodbye
+    ////////////////////////////////////////////////////////////
+    if (mpiHelper.rank() == 0)
+        DumuxMessage::print(/*firstCall=*/false);
+
+    return 0;
+}
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/params.input b/test/multidomain/facet/1p_1p/box_dof_enrichment/params.input
new file mode 100644
index 0000000000000000000000000000000000000000..384b9f365d8c0340189830345c42d8371d7d9b4c
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/params.input
@@ -0,0 +1,21 @@
+[Problem]
+EnableGravity = false
+FractureAperture = 1e-3
+
+[Grid]
+File = ./grids/extended_fracture.msh
+
+[Bulk]
+Problem.Name = bulk
+SpatialParams.Permeability = 1
+
+[LowDim]
+Problem.Name = lowdim
+SpatialParams.Permeability = 1e-13
+
+[Assembly]
+NumericDifference.BaseEpsilon = 1e3
+
+[Component]
+LiquidDensity = 1.0
+LiquidKinematicViscosity = 1.0
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/problem_bulk.hh b/test/multidomain/facet/1p_1p/box_dof_enrichment/problem_bulk.hh
new file mode 100644
index 0000000000000000000000000000000000000000..532bf9a94b785ab9023765d32e9bd28ce998493f
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/problem_bulk.hh
@@ -0,0 +1,113 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup FacetTests
+ * \brief The problem for the bulk domain in the box-facet coupling dof enrichment test.
+ */
+#ifndef DUMUX_TEST_FACET_BOX_DOF_ENRICHMENT_ONEP_BULKPROBLEM_HH
+#define DUMUX_TEST_FACET_BOX_DOF_ENRICHMENT_ONEP_BULKPROBLEM_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/boundarytypes.hh>
+#include <dumux/common/numeqvector.hh>
+
+#include <dumux/porousmediumflow/problem.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup FacetTests
+ * \brief Test problem for the incompressible one-phase model
+ *        with coupling across the bulk grid facets.
+ */
+template<class TypeTag>
+class OnePBulkProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+
+    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+    using PrimaryVariables = typename GridVariables::PrimaryVariables;
+    using Scalar = typename GridVariables::Scalar;
+
+    using GridGeometry = typename GridVariables::GridGeometry;
+    using FVElementGeometry = typename GridGeometry::LocalView;
+    using SubControlVolume = typename GridGeometry::SubControlVolume;
+    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
+    using GridView = typename GridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+    using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>;
+    using CouplingManager = GetPropType<TypeTag, Properties::CouplingManager>;
+    using NumEqVector = Dumux::NumEqVector<PrimaryVariables>;
+
+    static constexpr int dimWorld = GridView::dimensionworld;
+
+public:
+    OnePBulkProblem(std::shared_ptr<const GridGeometry> gridGeometry,
+                    std::shared_ptr<typename ParentType::SpatialParams> spatialParams,
+                    std::shared_ptr<CouplingManager> couplingManager,
+                    const std::string& paramGroup = "")
+    : ParentType(gridGeometry, spatialParams, paramGroup)
+    , couplingManagerPtr_(couplingManager)
+    {
+        problemName_  =  getParam<std::string>("Vtk.OutputName") + "_" +
+                         getParamFromGroup<std::string>(this->paramGroup(), "Problem.Name");
+    }
+
+    //! The problem name.
+    const std::string& name() const
+    { return problemName_; }
+
+    //! Specifies the type of boundary condition at a given position.
+    BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+        if (globalPos[1] < 1e-6 || globalPos[1] > this->gridGeometry().bBoxMax()[1] - 1e-6)
+            values.setAllDirichlet();
+        return values;
+    }
+
+    //! Specifies the type of interior boundary condition at a given position.
+    BoundaryTypes interiorBoundaryTypes(const Element& element, const SubControlVolumeFace& scvf) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+        return values;
+    }
+
+    //! Evaluates the source term at a given position.
+    NumEqVector sourceAtPos(const GlobalPosition& globalPos) const
+    { return NumEqVector(0.0); }
+
+    //! Evaluates the Dirichlet boundary condition for a given position.
+    PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+    { return initialAtPos(globalPos); }
+
+    //! Evaluates the Neumann boundary condition for a boundary segment.
+    NumEqVector neumannAtPos(const GlobalPosition& globalPos) const
+    { return NumEqVector(0.0); }
+
+    //! Evaluates the initial conditions.
+    PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
+    { return PrimaryVariables(globalPos[dimWorld-1]); }
+
+    //! Returns reference to the coupling manager.
+    const CouplingManager& couplingManager() const
+    { return *couplingManagerPtr_; }
+
+private:
+    std::shared_ptr<CouplingManager> couplingManagerPtr_;
+    std::string problemName_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/problem_lowdim.hh b/test/multidomain/facet/1p_1p/box_dof_enrichment/problem_lowdim.hh
new file mode 100644
index 0000000000000000000000000000000000000000..0da66d751e487eb9e8132071c025d79ea710f60a
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/problem_lowdim.hh
@@ -0,0 +1,109 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup FacetTests
+ * \brief The problem for the lower-dimensional domain in the box-facet coupling dof enrichment test.
+ */
+#ifndef DUMUX_TEST_FACET_BOX_DOF_ENRICHMENT_ONEP_LOWDIMPROBLEM_HH
+#define DUMUX_TEST_FACET_BOX_DOF_ENRICHMENT_ONEP_LOWDIMPROBLEM_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/boundarytypes.hh>
+#include <dumux/common/numeqvector.hh>
+
+#include <dumux/porousmediumflow/problem.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup FacetTests
+ * \brief The lower-dimensional test problem for the incompressible
+ *        one-phase model with coupling across the bulk grid facets.
+ */
+template<class TypeTag>
+class OnePLowDimProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+
+    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+    using ElementVolumeVariables = typename GridVariables::GridVolumeVariables::LocalView;
+    using PrimaryVariables = typename GridVariables::PrimaryVariables;
+    using Scalar = typename GridVariables::Scalar;
+
+    using GridGeometry = typename GridVariables::GridGeometry;
+    using FVElementGeometry = typename GridGeometry::LocalView;
+    using SubControlVolume = typename GridGeometry::SubControlVolume;
+    using GridView = typename GridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+    using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>;
+    using CouplingManager = GetPropType<TypeTag, Properties::CouplingManager>;
+    using NumEqVector = Dumux::NumEqVector<PrimaryVariables>;
+
+    static constexpr int dimWorld = GridView::dimensionworld;
+
+public:
+    OnePLowDimProblem(std::shared_ptr<const GridGeometry> gridGeometry,
+                      std::shared_ptr<typename ParentType::SpatialParams> spatialParams,
+                      std::shared_ptr<CouplingManager> couplingManager,
+                      const std::string& paramGroup = "")
+    : ParentType(gridGeometry, spatialParams, paramGroup)
+    , couplingManagerPtr_(couplingManager)
+    {
+        problemName_  =  getParam<std::string>("Vtk.OutputName") + "_" +
+                         getParamFromGroup<std::string>(this->paramGroup(), "Problem.Name");
+    }
+
+    //! The problem name.
+    const std::string& name() const
+    { return problemName_; }
+
+    //! Specifies the type of boundary condition at a given position.
+    BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+        return values;
+    }
+
+    //! Evaluates the source term at a given position.
+    NumEqVector source(const Element& element,
+                       const FVElementGeometry& fvGeometry,
+                       const ElementVolumeVariables& elemVolVars,
+                       const SubControlVolume& scv) const
+    {
+        // evaluate sources from bulk domain
+        auto source = couplingManagerPtr_->evalSourcesFromBulk(element, fvGeometry, elemVolVars, scv);
+        source /= scv.volume()*elemVolVars[scv].extrusionFactor();
+        return source;
+    }
+
+    //! Evaluates the Dirichlet boundary condition for a given position.
+    PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+    { return initialAtPos(globalPos); }
+
+    //! Evaluates the initial conditions.
+    PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
+    {
+        return PrimaryVariables(0.0);
+    }
+
+    //! Returns reference to the coupling manager.
+    const CouplingManager& couplingManager() const
+    { return *couplingManagerPtr_; }
+
+private:
+    std::shared_ptr<CouplingManager> couplingManagerPtr_;
+    std::string problemName_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/properties.hh b/test/multidomain/facet/1p_1p/box_dof_enrichment/properties.hh
new file mode 100644
index 0000000000000000000000000000000000000000..de5a006f7d03454f5f29c60d228ea1e1e21ab9e0
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/properties.hh
@@ -0,0 +1,122 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup FacetTests
+ * \brief The properties for the box-facet coupling dof enrichment test.
+ */
+#ifndef DUMUX_TEST_FACET_BOX_DOF_ENRICHMENT_ONEP_PROPERTIES_HH
+#define DUMUX_TEST_FACET_BOX_DOF_ENRICHMENT_ONEP_PROPERTIES_HH
+
+#include <dune/alugrid/grid.hh>
+#include <dune/foamgrid/foamgrid.hh>
+
+#include <dumux/material/components/constant.hh>
+#include <dumux/material/fluidsystems/1pliquid.hh>
+#include <dumux/porousmediumflow/1p/model.hh>
+#include <dumux/discretization/box.hh>
+
+#include <dumux/multidomain/facet/box/properties.hh>
+#include <dumux/multidomain/facet/couplingmapper.hh>
+#include <dumux/multidomain/facet/couplingmanager.hh>
+#include <dumux/multidomain/traits.hh>
+
+#include "spatialparams.hh"
+#include "problem_bulk.hh"
+#include "problem_lowdim.hh"
+
+// default for the bulk grid type
+#ifndef BULKGRIDTYPE
+#define BULKGRIDTYPE Dune::ALUGrid<2, 2, Dune::simplex, Dune::conforming>
+#endif
+
+#ifndef LOWDIMGRIDTYPE
+#define LOWDIMGRIDTYPE Dune::FoamGrid<1, 2>
+#endif
+
+namespace Dumux::Properties {
+
+// create the type tag nodes
+namespace TTag {
+struct OnePBulk { using InheritsFrom = std::tuple<OneP>; };
+struct OnePBulkBox { using InheritsFrom = std::tuple<BoxFacetCouplingModel, OnePBulk>; };
+} // end namespace TTag
+
+// Set the grid type
+template<class TypeTag>
+struct Grid<TypeTag, TTag::OnePBulk> { using type = BULKGRIDTYPE; };
+// Set the problem type
+template<class TypeTag>
+struct Problem<TypeTag, TTag::OnePBulk> { using type = OnePBulkProblem<TypeTag>; };
+// set the spatial params
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::OnePBulk>
+{
+    using type = OnePSpatialParams< GetPropType<TypeTag, Properties::GridGeometry>,
+                                    GetPropType<TypeTag, Properties::Scalar> >;
+};
+
+// the fluid system
+template<class TypeTag>
+struct FluidSystem<TypeTag, TTag::OnePBulk>
+{
+private:
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+    using type = FluidSystems::OnePLiquid< Scalar, Components::Constant<1, Scalar> >;
+};
+
+// create the type tag nodes
+namespace TTag {
+struct OnePLowDim { using InheritsFrom = std::tuple<OneP>; };
+struct OnePLowDimBox { using InheritsFrom = std::tuple<OnePLowDim, BoxModel>; };
+} // end namespace TTag
+
+// Set the grid type
+template<class TypeTag>
+struct Grid<TypeTag, TTag::OnePLowDim> { using type = LOWDIMGRIDTYPE; };
+// Set the problem type
+template<class TypeTag>
+struct Problem<TypeTag, TTag::OnePLowDim> { using type = OnePLowDimProblem<TypeTag>; };
+// set the spatial params
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::OnePLowDim>
+{
+    using type = OnePSpatialParams< GetPropType<TypeTag, Properties::GridGeometry>,
+                                    GetPropType<TypeTag, Properties::Scalar> >;
+};
+
+// the fluid system
+template<class TypeTag>
+struct FluidSystem<TypeTag, TTag::OnePLowDim>
+{
+private:
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+    using type = FluidSystems::OnePLiquid< Scalar, Components::Constant<1, Scalar> >;
+};
+
+// obtain/define some types to be used below in the property definitions and in main
+template< class BulkTypeTag, class LowDimTypeTag >
+class TestTraits
+{
+    using BulkFVGridGeometry = GetPropType<BulkTypeTag, Properties::GridGeometry>;
+    using LowDimFVGridGeometry = GetPropType<LowDimTypeTag, Properties::GridGeometry>;
+public:
+    using MDTraits = Dumux::MultiDomainTraits<BulkTypeTag, LowDimTypeTag>;
+    using CouplingMapper = Dumux::FacetCouplingMapper<BulkFVGridGeometry, LowDimFVGridGeometry>;
+    using CouplingManager = Dumux::FacetCouplingManager<MDTraits, CouplingMapper>;
+};
+
+// set cm property in the sub-problems
+using Traits = TestTraits<TTag::OnePBulkBox, TTag::OnePLowDimBox>;
+template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePBulkBox> { using type = typename Traits::CouplingManager; };
+template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePLowDimBox> { using type = typename Traits::CouplingManager; };
+
+} // end namespace Dumux::Properties
+
+#endif
diff --git a/test/multidomain/facet/1p_1p/box_dof_enrichment/spatialparams.hh b/test/multidomain/facet/1p_1p/box_dof_enrichment/spatialparams.hh
new file mode 100644
index 0000000000000000000000000000000000000000..b18962e046c0039f83d2e20053fd4af5438d0ce5
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/box_dof_enrichment/spatialparams.hh
@@ -0,0 +1,64 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup FacetTests
+ * \brief The spatial parameters for the box-facet coupling dof enrichment test.
+ */
+#ifndef DUMUX_TEST_TPFAFACETCOUPLING_ONEP_SPATIALPARAMS_HH
+#define DUMUX_TEST_TPFAFACETCOUPLING_ONEP_SPATIALPARAMS_HH
+
+#include <dumux/porousmediumflow/fvspatialparams1p.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup FacetTests
+ * \brief The spatial parameters for the single-phase facet coupling test.
+ */
+template< class GridGeometry, class Scalar >
+class OnePSpatialParams
+: public FVPorousMediumFlowSpatialParamsOneP< GridGeometry, Scalar, OnePSpatialParams<GridGeometry, Scalar> >
+{
+    using ThisType = OnePSpatialParams< GridGeometry, Scalar >;
+    using ParentType = FVPorousMediumFlowSpatialParamsOneP< GridGeometry, Scalar, ThisType >;
+
+    using GridView = typename GridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+    //! Export the type used for permeabilities
+    using PermeabilityType = Scalar;
+
+    OnePSpatialParams(std::shared_ptr<const GridGeometry> gridGeometry, const std::string& paramGroup = "")
+    : ParentType(gridGeometry)
+    {
+        permeability_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Permeability");
+        extrusion_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Aperture", 1.0);
+    }
+
+    //! Function for defining the (intrinsic) permeability \f$[m^2]\f$.
+    PermeabilityType permeabilityAtPos(const GlobalPosition& globalPos) const
+    { return permeability_; }
+
+    //! Returns the porosity
+    Scalar porosityAtPos(const GlobalPosition& globalPos) const
+    { return 1.0; }
+
+    //! Sets the aperture as extrusion factor.
+    Scalar extrusionFactorAtPos(const GlobalPosition& globalPos) const
+    { return extrusion_; }
+
+private:
+    PermeabilityType permeability_;
+    Scalar extrusion_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/references/test_md_facet_1p1p_dof_enrichment_extended_fracture_bulk-reference.vtu b/test/references/test_md_facet_1p1p_dof_enrichment_extended_fracture_bulk-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..d09d0352e10e3f00cc1dcc4a6b8692eafc1fcba1
--- /dev/null
+++ b/test/references/test_md_facet_1p1p_dof_enrichment_extended_fracture_bulk-reference.vtu
@@ -0,0 +1,3437 @@
+<?xml version="1.0"?>
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diff --git a/test/references/test_md_facet_1p1p_dof_enrichment_extended_fracture_lowdim-reference.vtp b/test/references/test_md_facet_1p1p_dof_enrichment_extended_fracture_lowdim-reference.vtp
new file mode 100644
index 0000000000000000000000000000000000000000..12f092f51b284b53af89ce32e95ae20c3fc756ec
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diff --git a/test/references/test_md_facet_1p1p_dof_enrichment_short_fracture_lowdim-reference.vtp b/test/references/test_md_facet_1p1p_dof_enrichment_short_fracture_lowdim-reference.vtp
new file mode 100644
index 0000000000000000000000000000000000000000..36a769a89e4793571a80e954e760df2482d923dd
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