diff --git a/finat/ufl/mixedelement.py b/finat/ufl/mixedelement.py
index df45bce9..20c25353 100644
--- a/finat/ufl/mixedelement.py
+++ b/finat/ufl/mixedelement.py
@@ -13,7 +13,8 @@
 
 import numpy as np
 
-from ufl.cell import as_cell
+from ufl.cell import CellSequence, as_cell
+from ufl.domain import MeshSequence
 from finat.ufl.finiteelement import FiniteElement
 from finat.ufl.finiteelementbase import FiniteElementBase
 from ufl.permutation import compute_indices
@@ -39,18 +40,6 @@ def __init__(self, *elements, **kwargs):
         elements = [MixedElement(e) if isinstance(e, (tuple, list)) else e
                     for e in elements]
         self._sub_elements = elements
-
-        # Pick the first cell, for now all should be equal
-        cells = tuple(sorted(set(element.cell for element in elements) - set([None])))
-        self._cells = cells
-        if cells:
-            cell = cells[0]
-            # Require that all elements are defined on the same cell
-            if not all(c == cell for c in cells[1:]):
-                raise ValueError("Sub elements must live on the same cell.")
-        else:
-            cell = None
-
         # Check that all elements use the same quadrature scheme TODO:
         # We can allow the scheme not to be defined.
         if len(elements) == 0:
@@ -70,9 +59,16 @@ def __init__(self, *elements, **kwargs):
         # Initialize element data
         degrees = {e.degree() for e in self._sub_elements} - {None}
         degree = max_degree(degrees) if degrees else None
-        FiniteElementBase.__init__(self, "Mixed", cell, degree, quad_scheme,
+        FiniteElementBase.__init__(self, "Mixed", self._make_cell(), degree, quad_scheme,
                                    reference_value_shape)
 
+    def _make_cell(self):
+        if self.num_sub_elements == 0:
+            return
+        else:
+            cells = tuple(e.cell for e in self.sub_elements)
+            return CellSequence(cells)
+
     def __repr__(self):
         """Doc."""
         return "MixedElement(" + ", ".join(repr(e) for e in self._sub_elements) + ")"
@@ -94,6 +90,8 @@ def symmetry(self, domain):
         :math:`c_1`.
         A component is a tuple of one or more ints.
         """
+        if isinstance(domain, MeshSequence):
+            raise NotImplementedError
         # Build symmetry map from symmetries of subelements
         sm = {}
         # Base index of the current subelement into mixed value
@@ -140,6 +138,8 @@ def extract_subelement_component(self, domain, i):
 
         component index for a given component index.
         """
+        if isinstance(domain, MeshSequence):
+            raise NotImplementedError
         if isinstance(i, int):
             i = (i,)
         self._check_component(i)
@@ -245,7 +245,16 @@ def embedded_superdegree(self):
 
     def reconstruct(self, **kwargs):
         """Doc."""
-        return MixedElement(*[e.reconstruct(**kwargs) for e in self.sub_elements])
+        cell = kwargs.pop('cell', None)
+        if cell is None:
+            cell = self.cell
+        else:
+            if not isinstance(cell, CellSequence):
+                # Allow for passing a single base cell.
+                cell = CellSequence([cell] * len(self.sub_elements))
+        return type(self)(
+            *[e.reconstruct(cell=c, **kwargs) for c, e in zip(cell.cells, self.sub_elements)],
+        )
 
     def variant(self):
         """Doc."""
@@ -307,8 +316,10 @@ def __init__(self, family, cell=None, degree=None, dim=None,
         reference_value_shape = (dim,) + sub_element.reference_value_shape
 
         # Initialize element data
-        MixedElement.__init__(self, sub_elements,
-                              reference_value_shape=reference_value_shape)
+        MixedElement.__init__(
+            self, sub_elements,
+            reference_value_shape=reference_value_shape,
+        )
 
         FiniteElementBase.__init__(self, sub_element.family(), sub_element.cell, sub_element.degree(),
                                    sub_element.quadrature_scheme(), reference_value_shape)
@@ -323,6 +334,13 @@ def __init__(self, family, cell=None, degree=None, dim=None,
         # Cache repr string
         self._repr = f"VectorElement({repr(sub_element)}, dim={dim}{var_str})"
 
+    def _make_cell(self):
+        if self.num_sub_elements == 0:
+            return
+        else:
+            cell, = set(e.cell for e in self.sub_elements)
+            return cell
+
     def __repr__(self):
         """Doc."""
         return self._repr
@@ -435,8 +453,10 @@ def __init__(self, family, cell=None, degree=None, shape=None,
 
         reference_value_shape = reference_value_shape + sub_element.reference_value_shape
         # Initialize element data
-        MixedElement.__init__(self, sub_elements,
-                              reference_value_shape=reference_value_shape)
+        MixedElement.__init__(
+            self, sub_elements,
+            reference_value_shape=reference_value_shape,
+        )
         self._family = sub_element.family()
         self._degree = sub_element.degree()
         self._sub_element = sub_element
@@ -454,6 +474,13 @@ def __init__(self, family, cell=None, degree=None, shape=None,
         self._repr = (f"TensorElement({repr(sub_element)}, shape={shape}, "
                       f"symmetry={symmetry}{var_str})")
 
+    def _make_cell(self):
+        if self.num_sub_elements == 0:
+            return
+        else:
+            cell, = set(e.cell for e in self.sub_elements)
+            return cell
+
     @property
     def pullback(self):
         """Get pull back."""