diff --git a/pandas/core/indexes/api.py b/pandas/core/indexes/api.py
index d4f22e482af84..76216f19b3ecb 100644
--- a/pandas/core/indexes/api.py
+++ b/pandas/core/indexes/api.py
@@ -135,13 +135,20 @@ def _get_combined_index(
     indexes = _get_distinct_objs(indexes)
     if len(indexes) == 0:
         index = Index([])
-    elif len(indexes) == 1:
+    elif len(indexes) == 1 or all_indexes_same(indexes):
         index = indexes[0]
     elif intersect:
+        duplicates = union_indexes(
+            [index[index.duplicated(keep="first")] for index in indexes]
+        )
         index = indexes[0]
         for other in indexes[1:]:
             index = index.intersection(other)
+        if len(duplicates.intersection(index)) > 0:
+            raise InvalidIndexError("Duplicated values in intersection of indices.")
     else:
+        if not all(idx.is_unique for idx in indexes):
+            raise InvalidIndexError("Cannot union indices with duplicate values.")
         index = union_indexes(indexes, sort=sort)
         index = ensure_index(index)
 
diff --git a/pandas/tests/indexes/test_setops.py b/pandas/tests/indexes/test_setops.py
index 538e937703de6..8a852a8dd4a9a 100644
--- a/pandas/tests/indexes/test_setops.py
+++ b/pandas/tests/indexes/test_setops.py
@@ -5,6 +5,8 @@
 import numpy as np
 import pytest
 
+from pandas.errors import InvalidIndexError
+
 from pandas.core.dtypes.common import is_dtype_equal
 
 import pandas as pd
@@ -21,6 +23,7 @@
 )
 import pandas._testing as tm
 from pandas.api.types import is_datetime64tz_dtype, pandas_dtype
+from pandas.core.indexes.api import get_objs_combined_axis
 
 COMPATIBLE_INCONSISTENT_PAIRS = {
     (Int64Index, RangeIndex): (tm.makeIntIndex, tm.makeRangeIndex),
@@ -463,3 +466,41 @@ def test_setop_with_categorical(index, sort, method):
     result = getattr(index, method)(other[:5], sort=sort)
     expected = getattr(index, method)(index[:5], sort=sort)
     tm.assert_index_equal(result, expected)
+
+
+@pytest.mark.parametrize("reverse", [True, False])
+def test_valid_intersection_w_dupes(index, reverse):
+    # Make sure base index is unique and has at least 3 values
+    index = index.unique()
+    if len(index) < 3:
+        pytest.skip()
+
+    series = [
+        pd.Series(1, index=index[[0, 0, 1, 2]]),
+        pd.Series(0, index=index[[1, 2]]),
+    ]
+    if reverse:
+        series = reversed(series)
+
+    result = get_objs_combined_axis(series, intersect=True)
+    expected = index[[1, 2]]
+
+    tm.assert_index_equal(result, expected, check_order=False)
+
+
+@pytest.mark.parametrize("reverse", [True, False])
+def test_invalid_intersection_w_dupes(index, reverse):
+    # Make sure base index is unique and has at least 3 values
+    index = index.unique()
+    if len(index) < 3:
+        pytest.skip()
+
+    series = [
+        pd.Series(1, index=index[[0, 0, 1, 2]]),
+        pd.Series(0, index=index[[0, 2]]),
+    ]
+    if reverse:
+        series = reversed(series)
+
+    with pytest.raises(InvalidIndexError):
+        _ = get_objs_combined_axis(series, intersect=True)
diff --git a/pandas/tests/reshape/concat/test_concat.py b/pandas/tests/reshape/concat/test_concat.py
index 16c4e9456aa05..fd3a9a00fee8a 100644
--- a/pandas/tests/reshape/concat/test_concat.py
+++ b/pandas/tests/reshape/concat/test_concat.py
@@ -5,6 +5,8 @@
 import numpy as np
 import pytest
 
+from pandas.errors import InvalidIndexError
+
 import pandas as pd
 from pandas import DataFrame, Index, MultiIndex, Series, concat, date_range
 import pandas._testing as tm
@@ -445,6 +447,57 @@ def test_concat_ordered_dict(self):
         tm.assert_series_equal(result, expected)
 
 
+@pytest.mark.parametrize("join", ["inner", "outer"])
+def test_concat_duplicates_error(index, join):
+    # https://github.com/pandas-dev/pandas/issues/6963
+    # Needs an index with 4 unique values
+    index = index.unique()
+    if len(index) < 4:
+        pytest.skip()
+
+    index_unique = index[:4]
+    index_non_unique = index_unique[[0, 0, 1, 2, 3]]
+
+    df_non_unique = DataFrame(
+        np.ones((1, len(index_non_unique))), columns=index_non_unique
+    )
+    df_unique = DataFrame(np.ones((1, len(index_unique))), columns=index_unique)
+
+    with pytest.raises(InvalidIndexError):
+        _ = pd.concat([df_non_unique, df_unique], join=join)
+
+
+@pytest.mark.xfail(reason="Not implemented")
+def test_concat_intersection_duplicates(index):
+    # ailing: https://github.com/pandas-dev/pandas/pull/38745/files#r549577521
+    # Concat is valid if the intersection does not contain duplicates
+    # Needs an index with 4 unique values
+    index = index.unique()
+    if len(index) < 4:
+        pytest.skip()
+
+    index_unique = index[[0, 1, 2]]
+    index_non_unique = index[[1, 2, 3, 3]]
+
+    df_unique = DataFrame(
+        np.ones((1, len(index_unique))),
+        columns=index_unique,
+    )
+    df_non_unique = DataFrame(
+        np.zeros((1, len(index_non_unique))),
+        columns=index_non_unique,
+    )
+
+    result = pd.concat([df_unique, df_non_unique], join="inner")
+    expected = DataFrame(
+        [[1, 1], [0, 0]],
+        columns=index[[1, 2]],
+        index=[0, 0],
+    )
+
+    tm.assert_frame_equal(result, expected)
+
+
 @pytest.mark.parametrize("pdt", [Series, pd.DataFrame])
 @pytest.mark.parametrize("dt", np.sctypes["float"])
 def test_concat_no_unnecessary_upcast(dt, pdt):