diff --git a/xarray/core/groupby.py b/xarray/core/groupby.py
index 827c0a3588f..77ea1b341c9 100644
--- a/xarray/core/groupby.py
+++ b/xarray/core/groupby.py
@@ -173,11 +173,12 @@ def _inverse_permutation_indices(positions, N: int | None = None) -> np.ndarray
 
     if isinstance(positions[0], slice):
         positions = _consolidate_slices(positions)
-        if positions == slice(None):
+        if positions == [slice(None)] or positions == [slice(0, None)]:
             return None
         positions = [np.arange(sl.start, sl.stop, sl.step) for sl in positions]
-
-    newpositions = nputils.inverse_permutation(np.concatenate(positions), N)
+    newpositions = nputils.inverse_permutation(
+        np.concatenate(tuple(p for p in positions if len(p) > 0)), N
+    )
     return newpositions[newpositions != -1]
 
 
@@ -990,7 +991,7 @@ def _maybe_reindex(self, combined):
             if (has_missing_groups and index is not None) or (
                 len(self.groupers) > 1
                 and not isinstance(grouper.full_index, pd.RangeIndex)
-                and not index.index.equals(grouper.full_index)
+                and not (index is not None and index.index.equals(grouper.full_index))
             ):
                 indexers[grouper.name] = grouper.full_index
         if indexers:
diff --git a/xarray/tests/test_groupby.py b/xarray/tests/test_groupby.py
index 47ea2fcd2b0..5075fa12b92 100644
--- a/xarray/tests/test_groupby.py
+++ b/xarray/tests/test_groupby.py
@@ -3850,6 +3850,20 @@ def test_groupby_bins_mean_time_series():
     assert ds_agged.time.dtype == np.dtype("datetime64[ns]")
 
 
+def test_groupby_multi_map():
+    # https://github.com/pydata/xarray/issues/11004
+    d = xr.DataArray(
+        [[0, 1], [2, 3]],
+        coords={
+            "lon": (["ny", "nx"], [[30, 40], [40, 50]]),
+            "lat": (["ny", "nx"], [[10, 10], [20, 20]]),
+        },
+        dims=["ny", "nx"],
+    )
+    xr.testing.assert_equal(d, d.groupby("lon").map(lambda x: x))
+    xr.testing.assert_equal(d, d.groupby(("lon", "lat")).map(lambda x: x))
+
+
 # TODO: Possible property tests to add to this module
 # 1. lambda x: x
 # 2. grouped-reduce on unique coords is identical to array