diff --git a/doc/release_notes.rst b/doc/release_notes.rst
index 993ce7c8..787b9901 100644
--- a/doc/release_notes.rst
+++ b/doc/release_notes.rst
@@ -112,6 +112,7 @@ Files from earlier versions load as before.
 * Adding or removing variables after ``freeze=True`` no longer breaks ``model.matrices`` with ``inconsistent shapes``. (`#926 <https://github.com/PyPSA/linopy/issues/926>`__)
 * A ``CSRConstraint`` from a CSR-backed expression keeps its auxiliary coordinates through ``to_dense()``, ``freeze()`` and netcdf. (`#941 <https://github.com/PyPSA/linopy/issues/941>`__)
 * Unsupported ``CSRConstraint`` operations (``loc``, ``update``, ``from_rule``, setting ``coeffs``/``vars``/``sign``) raise an ``AttributeError`` that points to ``.mutable()``. (`#963 <https://github.com/PyPSA/linopy/issues/963>`__)
+* Freezing a constraint with a ``MultiIndex`` dimension no longer raises ``TypeError: Must pass list-like as `names```.
 * Repeated matrix builds on an unchanged model reuse the cached column mapping again, so persistent snapshot diffs skip untouched frozen constraints. (`#933 <https://github.com/PyPSA/linopy/issues/933>`__)
 
 *Expressions*
diff --git a/linopy/csr.py b/linopy/csr.py
index 7c27463a..3a5f3f16 100644
--- a/linopy/csr.py
+++ b/linopy/csr.py
@@ -92,7 +92,7 @@ def from_coords(cls, coords: Iterable[pd.Index]) -> Grid:
     def from_dataset(cls, ds: Dataset | DataArray, dims: Iterable[str]) -> Grid:
         """Build from the indexes and auxiliary coordinates ``ds`` carries on ``dims``."""
         dims = tuple(dims)
-        indexes = {d: ds.get_index(d).rename(d) for d in dims}
+        indexes = {d: _named(ds.get_index(d), d) for d in dims}
         return cls(indexes, _aux_coords(ds, set(dims)))
 
     @classmethod
@@ -373,7 +373,7 @@ def from_grouper(
         )
         for d in coord_dims:
             if d != member_dim:
-                indexes[d] = ds.get_index(d).rename(d)
+                indexes[d] = _named(ds.get_index(d), d)
         aux |= _aux_coords(ds, set(coord_dims) - {member_dim})
         grid = Grid({d: indexes[d] for d in grid_dims}, aux)
         if isinstance(source, Dataset):
@@ -837,6 +837,15 @@ def _readonly(values: np.ndarray) -> np.ndarray:
     return values
 
 
+def _named(index: pd.Index, dim: str) -> pd.Index:
+    """``index`` named after ``dim``, keeping the level names of a MultiIndex."""
+    if isinstance(index, pd.MultiIndex):
+        index = index.copy()
+        index.name = dim
+        return index
+    return index.rename(dim)
+
+
 def _aux_coords(ds: Dataset | DataArray, dims: set[str]) -> AuxCoords:
     """Scalar and one-dimensional auxiliary coordinates of ``ds`` lying on ``dims``."""
     aux: AuxCoords = {}
diff --git a/linopy/expressions.py b/linopy/expressions.py
index 197482ad..e0414483 100644
--- a/linopy/expressions.py
+++ b/linopy/expressions.py
@@ -1275,7 +1275,9 @@ def _add_constant_legacy(
             if is_nan_scalar(other):
                 check_user_nan()
             warn_legacy_absence(self.const)
-            return self.assign(const=self.const.fillna(0) + other)
+            return self.assign(
+                const=self.const.fillna(0) + cast("float | np.number", other)
+            )
         self_const, da, needs_reindex = self._broadcast_and_align(
             other, fill_value, join
         )
diff --git a/test/test_io.py b/test/test_io.py
index dabee6f5..b3566434 100644
--- a/test/test_io.py
+++ b/test/test_io.py
@@ -399,6 +399,24 @@ def test_model_to_netcdf_with_multiindex(
     assert_model_equal(m, p)
 
 
+def test_model_to_netcdf_with_multiindex_frozen_constraint(
+    model_with_multiindex: Model, tmp_path: Path
+) -> None:
+    from linopy.constraints import CSRConstraint
+
+    m = model_with_multiindex
+    x, y = m.variables["x-var"], m.variables["y-var"]
+    con = m.add_constraints(x + y, LESS_EQUAL, 10, name="frozen", freeze=True)
+    assert isinstance(con, CSRConstraint)
+
+    fn = tmp_path / "test.nc"
+    m.to_netcdf(fn)
+    p = read_netcdf(fn)
+
+    assert isinstance(p.constraints["frozen"], CSRConstraint)
+    assert_model_equal(m, p)
+
+
 # Regression for https://github.com/PyPSA/linopy/issues/525.
 def test_model_to_netcdf_with_multiindex_scipy_engine(
     model_with_multiindex: Model, tmp_path: Path