diff --git a/tests/test_dual_evaluation.py b/tests/test_dual_evaluation.py
index 461226c2..c02cb688 100644
--- a/tests/test_dual_evaluation.py
+++ b/tests/test_dual_evaluation.py
@@ -59,3 +59,16 @@ def test_ufl_only_shape_mismatch():
     assert to_element.value_shape == (2,)
     with pytest.raises(ValueError):
         compile_expression_dual_evaluation(expr, to_element, W.ufl_element())
+
+
+@pytest.mark.parametrize("modifier",
+                         [lambda x: x, ufl.VectorElement, ufl.TensorElement],
+                         ids=["scalar", "vector", "tensor"])
+def test_interpolate_zany_argument(modifier):
+    mesh = ufl.Mesh(ufl.VectorElement("P", ufl.triangle, 2))
+    V = ufl.FunctionSpace(mesh, modifier(ufl.FiniteElement("P", ufl.triangle, 1)))
+    Q = ufl.FunctionSpace(mesh, modifier(ufl.FiniteElement("Argyris", ufl.triangle, 5)))
+    expr = ufl.TestFunction(Q)
+    to_element = create_element(V.ufl_element())
+    kernel = compile_expression_dual_evaluation(expr, to_element, V.ufl_element())
+    assert kernel.needs_external_coords
diff --git a/tsfc/driver.py b/tsfc/driver.py
index e01f0820..79ee4f58 100644
--- a/tsfc/driver.py
+++ b/tsfc/driver.py
@@ -222,7 +222,10 @@ def compile_expression_dual_evaluation(expression, to_element, ufl_element, *,
     builder.set_coefficient_numbers(coefficient_numbers)
 
     needs_external_coords = False
-    if has_type(expression, GeometricQuantity) or any(fem.needs_coordinate_mapping(c.ufl_element()) for c in coefficients):
+    if has_type(expression, GeometricQuantity) or any(
+        fem.needs_coordinate_mapping(c.ufl_element())
+        for c in chain(coefficients, arguments)
+    ):
         # Create a fake coordinate coefficient for a domain.
         coords_coefficient = ufl.Coefficient(ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
         builder.domain_coordinate[domain] = coords_coefficient
diff --git a/tsfc/fem.py b/tsfc/fem.py
index 09882208..1639a6bc 100644
--- a/tsfc/fem.py
+++ b/tsfc/fem.py
@@ -31,6 +31,8 @@
 from gem.unconcatenate import unconcatenate
 from gem.utils import cached_property
 
+import finat
+from finat.finiteelementbase import FiniteElementBase
 from finat.physically_mapped import PhysicalGeometry, NeedsCoordinateMappingElement
 from finat.point_set import PointSet, PointSingleton
 from finat.quadrature import make_quadrature
@@ -246,12 +248,64 @@ def physical_vertices(self):
         return self.physical_points(vs)
 
 
+@singledispatch
 def needs_coordinate_mapping(element):
+    raise AssertionError(f"Don't know how to handle {type(element)}")
+
+
+@needs_coordinate_mapping.register(ufl.FiniteElementBase)
+def _needs_coordinate_mapping_ufl(element):
     """Does this UFL element require a CoordinateMapping for translation?"""
     if element.family() == 'Real':
         return False
     else:
-        return isinstance(create_element(element), NeedsCoordinateMappingElement)
+        return needs_coordinate_mapping(create_element(element))
+
+
+@needs_coordinate_mapping.register(NeedsCoordinateMappingElement)
+def _needs_coordinate_mapping_finat_needs_coordinate_mapping(element):
+    return True
+
+
+@needs_coordinate_mapping.register(FiniteElementBase)
+def _needs_coordinate_mapping_finat_base(element):
+    return False
+
+
+@needs_coordinate_mapping.register(finat.DiscontinuousElement)
+def _needs_coordinate_mapping_finat_discontinuous(element):
+    return needs_coordinate_mapping(element.element)
+
+
+@needs_coordinate_mapping.register(finat.FlattenedDimensions)
+def _needs_coordinate_mapping_finat_cube(element):
+    return needs_coordinate_mapping(element.product)
+
+
+@needs_coordinate_mapping.register(finat.TensorProductElement)
+def _needs_coordinate_mapping_finat_tpe(element):
+    return any(map(needs_coordinate_mapping, element.factors))
+
+
+@needs_coordinate_mapping.register(finat.TensorFiniteElement)
+def _needs_coordinate_mapping_finat_tfe(element):
+    return needs_coordinate_mapping(element.base_element)
+
+
+@needs_coordinate_mapping.register(finat.EnrichedElement)
+def _needs_coordinate_mapping_finat_enriched(element):
+    return any(map(needs_coordinate_mapping, element.elements))
+
+
+@needs_coordinate_mapping.register(finat.mixed.MixedSubElement)
+def _needs_coordinate_mapping_finat_mixed(element):
+    return needs_coordinate_mapping(element.element)
+
+
+@needs_coordinate_mapping.register(finat.HDivElement)
+@needs_coordinate_mapping.register(finat.HCurlElement)
+def _needs_coordinate_mapping_finat_hdivcurl(element):
+    return needs_coordinate_mapping(element.wrappee)
 
 
 class PointSetContext(ContextBase):