diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 15da1221c90..15d9210c3a6 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -47,6 +47,8 @@ Bug fixes
   :py:meth:`DataArray.to_index` for multi-index levels (convert to single index).
   (:issue:`6836`, :pull:`7105`)
   By `Benoît Bovy <https://github.com/benbovy>`_.
+- Support for open_dataset backends that return datasets containing multi-indexes (:issue:`7139`, :pull:`7150`)
+  By `Lukas Bindreiter <https://github.com/lukasbindreiter>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/backends/api.py b/xarray/backends/api.py
index 3e34af08e27..13bcf046ac3 100644
--- a/xarray/backends/api.py
+++ b/xarray/backends/api.py
@@ -234,7 +234,7 @@ def _get_mtime(filename_or_obj):
 
 def _protect_dataset_variables_inplace(dataset, cache):
     for name, variable in dataset.variables.items():
-        if name not in variable.dims:
+        if name not in dataset._indexes:
             # no need to protect IndexVariable objects
             data = indexing.CopyOnWriteArray(variable._data)
             if cache:
diff --git a/xarray/tests/test_backends_api.py b/xarray/tests/test_backends_api.py
index e14234bcaf9..efff86d7683 100644
--- a/xarray/tests/test_backends_api.py
+++ b/xarray/tests/test_backends_api.py
@@ -48,6 +48,25 @@ def open_dataset(
     assert_identical(expected, actual)
 
 
+def test_multiindex() -> None:
+    # GH7139
+    # Check that we properly handle backends that change index variables
+    dataset = xr.Dataset(coords={"coord1": ["A", "B"], "coord2": [1, 2]})
+    dataset = dataset.stack(z=["coord1", "coord2"])
+
+    class MultiindexBackend(xr.backends.BackendEntrypoint):
+        def open_dataset(
+            self,
+            filename_or_obj,
+            drop_variables=None,
+            **kwargs,
+        ) -> xr.Dataset:
+            return dataset.copy(deep=True)
+
+    loaded = xr.open_dataset("fake_filename", engine=MultiindexBackend)
+    assert_identical(dataset, loaded)
+
+
 class PassThroughBackendEntrypoint(xr.backends.BackendEntrypoint):
     """Access an object passed to the `open_dataset` method."""