diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index ec7f3200b682b..8a98b27486d90 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -1171,6 +1171,38 @@ def test_groupby_sum_below_mincount_nullable_integer():
     tm.assert_frame_equal(result, expected)
 
 
+def test_if_empty_multiindex():
+    # GH 32464
+    # Test if index after groupby with more then one column is always MultiIndex
+    a = DataFrame({"a": [1, 2], "b": [5, 6], "c": [8, 9]})
+
+    agg_1 = a.groupby(["a", "b"]).sum()
+    agg_2 = a.groupby(["a", "b", "c"]).sum()
+
+    expected = MultiIndex(
+        levels=[[1, 2], [5, 6]], codes=[[0, 1], [0, 1]], names=["a", "b"]
+    )
+    result = agg_1.index
+
+    tm.assert_index_equal(expected, result)
+
+    expected = MultiIndex(
+        levels=[[1, 2], [5, 6], [8, 9]],
+        codes=[[0, 1], [0, 1], [0, 1]],
+        names=["a", "b", "c"],
+    )
+    result = agg_2.index
+
+    # Tests if group by with all columns has a MultiIndex
+    tm.assert_index_equal(expected, result)
+
+    index_1 = agg_1.iloc[:, :0].index
+    index_2 = agg_2.droplevel("c").index
+
+    # Tests if both agreggations have multiindex
+    tm.assert_index_equal(index_1, index_2)
+
+
 def test_mean_on_timedelta():
     # GH 17382
     df = DataFrame({"time": pd.to_timedelta(range(10)), "cat": ["A", "B"] * 5})