diff --git a/pandas/tests/groupby/aggregate/test_aggregate.py b/pandas/tests/groupby/aggregate/test_aggregate.py
index c03ffe317083c..4313b52798c6e 100644
--- a/pandas/tests/groupby/aggregate/test_aggregate.py
+++ b/pandas/tests/groupby/aggregate/test_aggregate.py
@@ -495,6 +495,80 @@ def test_mangled(self):
         tm.assert_frame_equal(result, expected)
 
 
+@pytest.mark.parametrize(
+    "agg_col1, agg_col2, agg_col3, agg_result1, agg_result2, agg_result3",
+    [
+        (
+            (("y", "A"), "max"),
+            (("y", "A"), np.min),
+            (("y", "B"), "mean"),
+            [1, 3],
+            [0, 2],
+            [5.5, 7.5],
+        ),
+        (
+            (("y", "A"), lambda x: max(x)),
+            (("y", "A"), lambda x: 1),
+            (("y", "B"), "mean"),
+            [1, 3],
+            [1, 1],
+            [5.5, 7.5],
+        ),
+        (
+            pd.NamedAgg(("y", "A"), "max"),
+            pd.NamedAgg(("y", "B"), np.mean),
+            pd.NamedAgg(("y", "A"), lambda x: 1),
+            [1, 3],
+            [5.5, 7.5],
+            [1, 1],
+        ),
+    ],
+)
+def test_agg_relabel_multiindex_column(
+    agg_col1, agg_col2, agg_col3, agg_result1, agg_result2, agg_result3
+):
+    # GH 29422, add tests for multiindex column cases
+    df = DataFrame(
+        {"group": ["a", "a", "b", "b"], "A": [0, 1, 2, 3], "B": [5, 6, 7, 8]}
+    )
+    df.columns = pd.MultiIndex.from_tuples([("x", "group"), ("y", "A"), ("y", "B")])
+    idx = pd.Index(["a", "b"], name=("x", "group"))
+
+    result = df.groupby(("x", "group")).agg(a_max=(("y", "A"), "max"))
+    expected = DataFrame({"a_max": [1, 3]}, index=idx)
+    tm.assert_frame_equal(result, expected)
+
+    result = df.groupby(("x", "group")).agg(
+        col_1=agg_col1, col_2=agg_col2, col_3=agg_col3
+    )
+    expected = DataFrame(
+        {"col_1": agg_result1, "col_2": agg_result2, "col_3": agg_result3}, index=idx
+    )
+    tm.assert_frame_equal(result, expected)
+
+
+def test_agg_relabel_multiindex_raises_not_exist():
+    # GH 29422, add test for raises senario when aggregate column does not exist
+    df = DataFrame(
+        {"group": ["a", "a", "b", "b"], "A": [0, 1, 2, 3], "B": [5, 6, 7, 8]}
+    )
+    df.columns = pd.MultiIndex.from_tuples([("x", "group"), ("y", "A"), ("y", "B")])
+
+    with pytest.raises(KeyError, match="does not exist"):
+        df.groupby(("x", "group")).agg(a=(("Y", "a"), "max"))
+
+
+def test_agg_relabel_multiindex_raises_duplicate():
+    # GH29422, add test for raises senario when getting duplicates
+    df = DataFrame(
+        {"group": ["a", "a", "b", "b"], "A": [0, 1, 2, 3], "B": [5, 6, 7, 8]}
+    )
+    df.columns = pd.MultiIndex.from_tuples([("x", "group"), ("y", "A"), ("y", "B")])
+
+    with pytest.raises(SpecificationError, match="Function names"):
+        df.groupby(("x", "group")).agg(a=(("y", "A"), "min"), b=(("y", "A"), "min"))
+
+
 def myfunc(s):
     return np.percentile(s, q=0.90)