def METHOD_NAME() -> 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)