diff --git a/pandas/tests/indexes/multi/test_indexing.py b/pandas/tests/indexes/multi/test_indexing.py
index 6b27682ed5674..cf494b2ce87cc 100644
--- a/pandas/tests/indexes/multi/test_indexing.py
+++ b/pandas/tests/indexes/multi/test_indexing.py
@@ -3,7 +3,7 @@
 import numpy as np
 import pytest
 
-from pandas.errors import InvalidIndexError
+from pandas.errors import InvalidIndexError, PerformanceWarning
 
 import pandas as pd
 from pandas import Categorical, Index, MultiIndex, date_range
@@ -646,6 +646,22 @@ def test_get_loc_duplicates2(self):
 
         assert index.get_loc("D") == slice(0, 3)
 
+    def test_get_loc_past_lexsort_depth(self):
+        # GH#30053
+        idx = MultiIndex(
+            levels=[["a"], [0, 7], [1]],
+            codes=[[0, 0], [1, 0], [0, 0]],
+            names=["x", "y", "z"],
+            sortorder=0,
+        )
+        key = ("a", 7)
+
+        with tm.assert_produces_warning(PerformanceWarning):
+            # PerformanceWarning: indexing past lexsort depth may impact performance
+            result = idx.get_loc(key)
+
+        assert result == slice(0, 1, None)
+
 
 class TestWhere:
     def test_where(self):
diff --git a/pandas/tests/indexing/multiindex/test_loc.py b/pandas/tests/indexing/multiindex/test_loc.py
index 1b659bec0e9e8..518ec9e997183 100644
--- a/pandas/tests/indexing/multiindex/test_loc.py
+++ b/pandas/tests/indexing/multiindex/test_loc.py
@@ -522,3 +522,47 @@ def test_loc_with_mi_indexer():
         columns=["author", "price"],
     )
     tm.assert_frame_equal(result, expected)
+
+
+def test_getitem_str_slice(datapath):
+    # GH#15928
+    path = datapath("reshape", "merge", "data", "quotes2.csv")
+    df = pd.read_csv(path, parse_dates=["time"])
+    df2 = df.set_index(["ticker", "time"]).sort_index()
+
+    res = df2.loc[("AAPL", slice("2016-05-25 13:30:00")), :].droplevel(0)
+    expected = df2.loc["AAPL"].loc[slice("2016-05-25 13:30:00"), :]
+    tm.assert_frame_equal(res, expected)
+
+
+def test_3levels_leading_period_index():
+    # GH#24091
+    pi = pd.PeriodIndex(
+        ["20181101 1100", "20181101 1200", "20181102 1300", "20181102 1400"],
+        name="datetime",
+        freq="B",
+    )
+    lev2 = ["A", "A", "Z", "W"]
+    lev3 = ["B", "C", "Q", "F"]
+    mi = pd.MultiIndex.from_arrays([pi, lev2, lev3])
+
+    ser = pd.Series(range(4), index=mi, dtype=np.float64)
+    result = ser.loc[(pi[0], "A", "B")]
+    assert result == 0.0
+
+
+class TestKeyErrorsWithMultiIndex:
+    def test_missing_keys_raises_keyerror(self):
+        # GH#27420 KeyError, not TypeError
+        df = pd.DataFrame(np.arange(12).reshape(4, 3), columns=["A", "B", "C"])
+        df2 = df.set_index(["A", "B"])
+
+        with pytest.raises(KeyError, match="1"):
+            df2.loc[(1, 6)]
+
+    def test_missing_key_raises_keyerror2(self):
+        # GH#21168 KeyError, not "IndexingError: Too many indexers"
+        ser = pd.Series(-1, index=pd.MultiIndex.from_product([[0, 1]] * 2))
+
+        with pytest.raises(KeyError, match=r"\(0, 3\)"):
+            ser.loc[0, 3]