diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index d6ad5eb2003ce..583180d834010 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -498,6 +498,7 @@ Indexing
 - Bug in :meth:`DataFrame.nlargest` and :meth:`Series.nlargest` where sorted result did not count indexes containing ``np.nan`` (:issue:`28984`)
 - Bug in indexing on a non-unique object-dtype :class:`Index` with an NA scalar (e.g. ``np.nan``) (:issue:`43711`)
 - Bug in :meth:`Series.__setitem__` with object dtype when setting an array with matching size and dtype='datetime64[ns]' or dtype='timedelta64[ns]' incorrectly converting the datetime/timedeltas to integers (:issue:`43868`)
+- Bug in :meth:`Index.get_indexer_non_unique` when index contains multiple ``np.datetime64("NaT")`` and ``np.timedelta64("NaT")`` (:issue:`43869`)
 -
 
 Missing
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index 43fe9f1d091c8..92837a43e2b69 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -315,14 +315,14 @@ cdef class IndexEngine:
         missing : np.ndarray[np.intp]
         """
         cdef:
-            ndarray values, x
+            ndarray values
             ndarray[intp_t] result, missing
-            set stargets, remaining_stargets
+            set stargets, remaining_stargets, found_nas
             dict d = {}
             object val
             Py_ssize_t count = 0, count_missing = 0
             Py_ssize_t i, j, n, n_t, n_alloc, start, end
-            bint d_has_nan = False, stargets_has_nan = False, need_nan_check = True
+            bint check_na_values = False
 
         values = self.values
         stargets = set(targets)
@@ -357,33 +357,58 @@ cdef class IndexEngine:
         if stargets:
             # otherwise, map by iterating through all items in the index
 
+            # short-circuit na check
+            if values.dtype == object:
+                check_na_values = True
+                # keep track of nas in values
+                found_nas = set()
+
             for i in range(n):
                 val = values[i]
+
+                # GH#43870
+                # handle lookup for nas
+                # (ie. np.nan, float("NaN"), Decimal("NaN"), dt64nat, td64nat)
+                if check_na_values and checknull(val):
+                    match = [na for na in found_nas if is_matching_na(val, na)]
+
+                    # matching na not found
+                    if not len(match):
+                        found_nas.add(val)
+
+                        # add na to stargets to utilize `in` for stargets/d lookup
+                        match_stargets = [
+                            x for x in stargets if is_matching_na(val, x)
+                        ]
+
+                        if len(match_stargets):
+                            # add our 'standardized' na
+                            stargets.add(val)
+
+                    # matching na found
+                    else:
+                        assert len(match) == 1
+                        val = match[0]
+
                 if val in stargets:
                     if val not in d:
                         d[val] = []
                     d[val].append(i)
 
-                elif util.is_nan(val):
-                    # GH#35392
-                    if need_nan_check:
-                        # Do this check only once
-                        stargets_has_nan = any(util.is_nan(val) for x in stargets)
-                        need_nan_check = False
-
-                    if stargets_has_nan:
-                        if not d_has_nan:
-                            # use a canonical nan object
-                            d[np.nan] = []
-                            d_has_nan = True
-                        d[np.nan].append(i)
-
         for i in range(n_t):
             val = targets[i]
 
+            # ensure there are nas in values before looking for a matching na
+            if check_na_values and checknull(val):
+                match = [na for na in found_nas if is_matching_na(val, na)]
+                if len(match):
+                    assert len(match) == 1
+                    val = match[0]
+
             # found
-            if val in d or (d_has_nan and util.is_nan(val)):
-                key = val if not util.is_nan(val) else np.nan
+            if val in d:
+                key = val
+
                 for j in d[key]:
 
                     # realloc if needed
diff --git a/pandas/_libs/missing.pyx b/pandas/_libs/missing.pyx
index cbe79d11fbfc9..90f409d371e6b 100644
--- a/pandas/_libs/missing.pyx
+++ b/pandas/_libs/missing.pyx
@@ -20,9 +20,12 @@ from pandas._libs cimport util
 from pandas._libs.tslibs.nattype cimport (
     c_NaT as NaT,
     checknull_with_nat,
+    is_dt64nat,
     is_null_datetimelike,
+    is_td64nat,
 )
 from pandas._libs.tslibs.np_datetime cimport (
+    get_datetime64_unit,
     get_datetime64_value,
     get_timedelta64_value,
 )
@@ -82,12 +85,14 @@ cpdef bint is_matching_na(object left, object right, bint nan_matches_none=False
             get_datetime64_value(left) == NPY_NAT
             and util.is_datetime64_object(right)
             and get_datetime64_value(right) == NPY_NAT
+            and get_datetime64_unit(left) == get_datetime64_unit(right)
         )
     elif util.is_timedelta64_object(left):
         return (
             get_timedelta64_value(left) == NPY_NAT
             and util.is_timedelta64_object(right)
             and get_timedelta64_value(right) == NPY_NAT
+            and get_datetime64_unit(left) == get_datetime64_unit(right)
         )
     elif is_decimal_na(left):
         return is_decimal_na(right)
@@ -345,20 +350,16 @@ def isneginf_scalar(val: object) -> bool:
 cdef inline bint is_null_datetime64(v):
     # determine if we have a null for a datetime (or integer versions),
     # excluding np.timedelta64('nat')
-    if checknull_with_nat(v):
+    if checknull_with_nat(v) or is_dt64nat(v):
         return True
-    elif util.is_datetime64_object(v):
-        return get_datetime64_value(v) == NPY_NAT
     return False
 
 
 cdef inline bint is_null_timedelta64(v):
     # determine if we have a null for a timedelta (or integer versions),
     # excluding np.datetime64('nat')
-    if checknull_with_nat(v):
+    if checknull_with_nat(v) or is_td64nat(v):
         return True
-    elif util.is_timedelta64_object(v):
-        return get_timedelta64_value(v) == NPY_NAT
     return False
 
 
diff --git a/pandas/_libs/tslibs/nattype.pxd b/pandas/_libs/tslibs/nattype.pxd
index d38f4518f9bf0..35319bd88053a 100644
--- a/pandas/_libs/tslibs/nattype.pxd
+++ b/pandas/_libs/tslibs/nattype.pxd
@@ -16,4 +16,6 @@ cdef _NaT c_NaT
 
 
 cdef bint checknull_with_nat(object val)
+cdef bint is_dt64nat(object val)
+cdef bint is_td64nat(object val)
 cpdef bint is_null_datetimelike(object val, bint inat_is_null=*)
diff --git a/pandas/_libs/tslibs/nattype.pyx b/pandas/_libs/tslibs/nattype.pyx
index 521927cd910ec..23094bdb90483 100644
--- a/pandas/_libs/tslibs/nattype.pyx
+++ b/pandas/_libs/tslibs/nattype.pyx
@@ -1133,6 +1133,22 @@ cdef inline bint checknull_with_nat(object val):
     """
     return val is None or util.is_nan(val) or val is c_NaT
 
+cdef inline bint is_dt64nat(object val):
+    """
+    Is this a np.datetime64 object np.datetime64("NaT").
+    """
+    if util.is_datetime64_object(val):
+        return get_datetime64_value(val) == NPY_NAT
+    return False
+
+cdef inline bint is_td64nat(object val):
+    """
+    Is this a np.timedelta64 object np.timedelta64("NaT").
+    """
+    if util.is_timedelta64_object(val):
+        return get_timedelta64_value(val) == NPY_NAT
+    return False
+
 
 cpdef bint is_null_datetimelike(object val, bint inat_is_null=True):
     """
diff --git a/pandas/_testing/__init__.py b/pandas/_testing/__init__.py
index c54185e324646..e8283a222d86a 100644
--- a/pandas/_testing/__init__.py
+++ b/pandas/_testing/__init__.py
@@ -157,6 +157,25 @@
 )
 
 NULL_OBJECTS = [None, np.nan, pd.NaT, float("nan"), pd.NA, Decimal("NaN")]
+NP_NAT_OBJECTS = [
+    cls("NaT", unit)
+    for cls in [np.datetime64, np.timedelta64]
+    for unit in [
+        "Y",
+        "M",
+        "W",
+        "D",
+        "h",
+        "m",
+        "s",
+        "ms",
+        "us",
+        "ns",
+        "ps",
+        "fs",
+        "as",
+    ]
+]
 
 EMPTY_STRING_PATTERN = re.compile("^$")
 
diff --git a/pandas/conftest.py b/pandas/conftest.py
index 44b805c632723..75711b19dfcfd 100644
--- a/pandas/conftest.py
+++ b/pandas/conftest.py
@@ -332,6 +332,19 @@ def unique_nulls_fixture(request):
 # Generate cartesian product of unique_nulls_fixture:
 unique_nulls_fixture2 = unique_nulls_fixture
 
+
+@pytest.fixture(params=tm.NP_NAT_OBJECTS, ids=lambda x: type(x).__name__)
+def np_nat_fixture(request):
+    """
+    Fixture for each NaT type in numpy.
+    """
+    return request.param
+
+
+# Generate cartesian product of np_nat_fixture:
+np_nat_fixture2 = np_nat_fixture
+
+
 # ----------------------------------------------------------------
 # Classes
 # ----------------------------------------------------------------
diff --git a/pandas/tests/indexes/object/test_indexing.py b/pandas/tests/indexes/object/test_indexing.py
index 039483cc948df..38bd96921b991 100644
--- a/pandas/tests/indexes/object/test_indexing.py
+++ b/pandas/tests/indexes/object/test_indexing.py
@@ -1,3 +1,5 @@
+from decimal import Decimal
+
 import numpy as np
 import pytest
 
@@ -90,12 +92,63 @@ def test_get_indexer_non_unique_nas(self, nulls_fixture):
         # matching-but-not-identical nans
         if is_matching_na(nulls_fixture, float("NaN")):
             index = Index(["a", float("NaN"), "b", float("NaN")])
+            match_but_not_identical = True
+        elif is_matching_na(nulls_fixture, Decimal("NaN")):
+            index = Index(["a", Decimal("NaN"), "b", Decimal("NaN")])
+            match_but_not_identical = True
+        else:
+            match_but_not_identical = False
+
+        if match_but_not_identical:
             indexer, missing = index.get_indexer_non_unique([nulls_fixture])
 
             expected_indexer = np.array([1, 3], dtype=np.intp)
             tm.assert_numpy_array_equal(indexer, expected_indexer)
             tm.assert_numpy_array_equal(missing, expected_missing)
 
+    @pytest.mark.filterwarnings("ignore:elementwise comp:DeprecationWarning")
+    def test_get_indexer_non_unique_np_nats(self, np_nat_fixture, np_nat_fixture2):
+        expected_missing = np.array([], dtype=np.intp)
+        # matching-but-not-identical nats
+        if is_matching_na(np_nat_fixture, np_nat_fixture2):
+            # ensure nats are different objects
+            index = Index(
+                np.array(
+                    ["2021-10-02", np_nat_fixture.copy(), np_nat_fixture2.copy()],
+                    dtype=object,
+                ),
+                dtype=object,
+            )
+            # pass as index to prevent target from being casted to DatetimeIndex
+            indexer, missing = index.get_indexer_non_unique(
+                Index([np_nat_fixture], dtype=object)
+            )
+            expected_indexer = np.array([1, 2], dtype=np.intp)
+            tm.assert_numpy_array_equal(indexer, expected_indexer)
+            tm.assert_numpy_array_equal(missing, expected_missing)
+        # dt64nat vs td64nat
+        else:
+            index = Index(
+                np.array(
+                    [
+                        "2021-10-02",
+                        np_nat_fixture,
+                        np_nat_fixture2,
+                        np_nat_fixture,
+                        np_nat_fixture2,
+                    ],
+                    dtype=object,
+                ),
+                dtype=object,
+            )
+            # pass as index to prevent target from being casted to DatetimeIndex
+            indexer, missing = index.get_indexer_non_unique(
+                Index([np_nat_fixture], dtype=object)
+            )
+            expected_indexer = np.array([1, 3], dtype=np.intp)
+            tm.assert_numpy_array_equal(indexer, expected_indexer)
+            tm.assert_numpy_array_equal(missing, expected_missing)
+
 
 class TestSliceLocs:
     @pytest.mark.parametrize(
diff --git a/pandas/tests/indexes/test_indexing.py b/pandas/tests/indexes/test_indexing.py
index ff2cd76ab6377..0a001008c2f1b 100644
--- a/pandas/tests/indexes/test_indexing.py
+++ b/pandas/tests/indexes/test_indexing.py
@@ -320,6 +320,11 @@ def test_maybe_cast_slice_bound_kind_deprecated(index):
             np.array([1, 2], dtype=np.intp),
         ),
         (["a", "b", "a", np.nan], [np.nan], np.array([3], dtype=np.intp)),
+        (
+            np.array(["b", np.nan, float("NaN"), "b"], dtype=object),
+            Index([np.nan], dtype=object),
+            np.array([1, 2], dtype=np.intp),
+        ),
     ],
 )
 def test_get_indexer_non_unique_multiple_nans(idx, target, expected):