diff --git a/doc/source/whatsnew/v0.24.0.rst b/doc/source/whatsnew/v0.24.0.rst
index 4e12b22c8ccac..4ea67d1c883db 100644
--- a/doc/source/whatsnew/v0.24.0.rst
+++ b/doc/source/whatsnew/v0.24.0.rst
@@ -1146,7 +1146,9 @@ from :class:`Period`, :class:`PeriodIndex`, and in some cases
 :class:`Timestamp`, :class:`DatetimeIndex` and :class:`TimedeltaIndex`.
 
 This usage is now deprecated.  Instead add or subtract integer multiples of
-the object's ``freq`` attribute (:issue:`21939`)
+the object's ``freq`` attribute. The result of subtraction of :class:`Period`
+objects will be agnostic of the multiplier of the objects' ``freq`` attribute
+(:issue:`21939`, :issue:`23878`).
 
 Previous Behavior:
 
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index f3ac102bf177e..7685ddd76d4b6 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -352,6 +352,14 @@ class _BaseOffset(object):
                 if name not in ['n', 'normalize']}
         return {name: kwds[name] for name in kwds if kwds[name] is not None}
 
+    @property
+    def base(self):
+        """
+        Returns a copy of the calling offset object with n=1 and all other
+        attributes equal.
+        """
+        return type(self)(n=1, normalize=self.normalize, **self.kwds)
+
     def __add__(self, other):
         if getattr(other, "_typ", None) in ["datetimeindex", "periodindex",
                                             "datetimearray", "periodarray",
diff --git a/pandas/_libs/tslibs/period.pyx b/pandas/_libs/tslibs/period.pyx
index dfbf24cf177f6..1ad2688b70a03 100644
--- a/pandas/_libs/tslibs/period.pyx
+++ b/pandas/_libs/tslibs/period.pyx
@@ -1686,7 +1686,8 @@ cdef class _Period(object):
                 if other.freq != self.freq:
                     msg = _DIFFERENT_FREQ.format(self.freqstr, other.freqstr)
                     raise IncompatibleFrequency(msg)
-                return (self.ordinal - other.ordinal) * self.freq
+                # GH 23915 - mul by base freq since __add__ is agnostic of n
+                return (self.ordinal - other.ordinal) * self.freq.base
             elif getattr(other, '_typ', None) == 'periodindex':
                 # GH#21314 PeriodIndex - Period returns an object-index
                 # of DateOffset objects, for which we cannot use __neg__
diff --git a/pandas/conftest.py b/pandas/conftest.py
index 20f97bdec1107..c72efdf865052 100644
--- a/pandas/conftest.py
+++ b/pandas/conftest.py
@@ -636,6 +636,14 @@ def mock():
         return pytest.importorskip("mock")
 
 
+@pytest.fixture(params=[getattr(pd.offsets, o) for o in pd.offsets.__all__ if
+                        issubclass(getattr(pd.offsets, o), pd.offsets.Tick)])
+def tick_classes(request):
+    """
+    Fixture for Tick based datetime offsets available for a time series.
+    """
+    return request.param
+
 # ----------------------------------------------------------------
 # Global setup for tests using Hypothesis
 
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 45eec41e498d1..ceaf9e748fe5a 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -710,7 +710,7 @@ def _sub_period_array(self, other):
                                           arr_mask=self._isnan,
                                           b_mask=other._isnan)
 
-        new_values = np.array([self.freq * x for x in new_values])
+        new_values = np.array([self.freq.base * x for x in new_values])
         if self.hasnans or other.hasnans:
             mask = (self._isnan) | (other._isnan)
             new_values[mask] = NaT
diff --git a/pandas/tests/arithmetic/test_period.py b/pandas/tests/arithmetic/test_period.py
index 7158eae376ba6..9f436281de0a0 100644
--- a/pandas/tests/arithmetic/test_period.py
+++ b/pandas/tests/arithmetic/test_period.py
@@ -370,6 +370,41 @@ def test_parr_sub_pi_mismatched_freq(self, box_with_array):
         with pytest.raises(IncompatibleFrequency):
             rng - other
 
+    @pytest.mark.parametrize('n', [1, 2, 3, 4])
+    def test_sub_n_gt_1_ticks(self, tick_classes, n):
+        # GH 23878
+        p1_d = '19910905'
+        p2_d = '19920406'
+        p1 = pd.PeriodIndex([p1_d], freq=tick_classes(n))
+        p2 = pd.PeriodIndex([p2_d], freq=tick_classes(n))
+
+        expected = (pd.PeriodIndex([p2_d], freq=p2.freq.base)
+                    - pd.PeriodIndex([p1_d], freq=p1.freq.base))
+
+        tm.assert_index_equal((p2 - p1), expected)
+
+    @pytest.mark.parametrize('n', [1, 2, 3, 4])
+    @pytest.mark.parametrize('offset, kwd_name', [
+        (pd.offsets.YearEnd, 'month'),
+        (pd.offsets.QuarterEnd, 'startingMonth'),
+        (pd.offsets.MonthEnd, None),
+        (pd.offsets.Week, 'weekday')
+    ])
+    def test_sub_n_gt_1_offsets(self, offset, kwd_name, n):
+        # GH 23878
+        kwds = {kwd_name: 3} if kwd_name is not None else {}
+        p1_d = '19910905'
+        p2_d = '19920406'
+        freq = offset(n, normalize=False, **kwds)
+        p1 = pd.PeriodIndex([p1_d], freq=freq)
+        p2 = pd.PeriodIndex([p2_d], freq=freq)
+
+        result = p2 - p1
+        expected = (pd.PeriodIndex([p2_d], freq=freq.base)
+                    - pd.PeriodIndex([p1_d], freq=freq.base))
+
+        tm.assert_index_equal(result, expected)
+
     # -------------------------------------------------------------
     # Invalid Operations
 
diff --git a/pandas/tests/scalar/period/test_period.py b/pandas/tests/scalar/period/test_period.py
index ddb4f89738f98..715a596999e42 100644
--- a/pandas/tests/scalar/period/test_period.py
+++ b/pandas/tests/scalar/period/test_period.py
@@ -1106,6 +1106,38 @@ def test_sub(self):
         with pytest.raises(period.IncompatibleFrequency, match=msg):
             per1 - Period('2011-02', freq='M')
 
+    @pytest.mark.parametrize('n', [1, 2, 3, 4])
+    def test_sub_n_gt_1_ticks(self, tick_classes, n):
+        # GH 23878
+        p1 = pd.Period('19910905', freq=tick_classes(n))
+        p2 = pd.Period('19920406', freq=tick_classes(n))
+
+        expected = (pd.Period(str(p2), freq=p2.freq.base)
+                    - pd.Period(str(p1), freq=p1.freq.base))
+
+        assert (p2 - p1) == expected
+
+    @pytest.mark.parametrize('normalize', [True, False])
+    @pytest.mark.parametrize('n', [1, 2, 3, 4])
+    @pytest.mark.parametrize('offset, kwd_name', [
+        (pd.offsets.YearEnd, 'month'),
+        (pd.offsets.QuarterEnd, 'startingMonth'),
+        (pd.offsets.MonthEnd, None),
+        (pd.offsets.Week, 'weekday')
+    ])
+    def test_sub_n_gt_1_offsets(self, offset, kwd_name, n, normalize):
+        # GH 23878
+        kwds = {kwd_name: 3} if kwd_name is not None else {}
+        p1_d = '19910905'
+        p2_d = '19920406'
+        p1 = pd.Period(p1_d, freq=offset(n, normalize, **kwds))
+        p2 = pd.Period(p2_d, freq=offset(n, normalize, **kwds))
+
+        expected = (pd.Period(p2_d, freq=p2.freq.base)
+                    - pd.Period(p1_d, freq=p1.freq.base))
+
+        assert (p2 - p1) == expected
+
     def test_add_offset(self):
         # freq is DateOffset
         for freq in ['A', '2A', '3A']:
diff --git a/pandas/tests/tseries/offsets/conftest.py b/pandas/tests/tseries/offsets/conftest.py
index db8379e335679..c192a56b205ca 100644
--- a/pandas/tests/tseries/offsets/conftest.py
+++ b/pandas/tests/tseries/offsets/conftest.py
@@ -19,12 +19,3 @@ def month_classes(request):
     Fixture for month based datetime offsets available for a time series.
     """
     return request.param
-
-
-@pytest.fixture(params=[getattr(offsets, o) for o in offsets.__all__ if
-                        issubclass(getattr(offsets, o), offsets.Tick)])
-def tick_classes(request):
-    """
-    Fixture for Tick based datetime offsets available for a time series.
-    """
-    return request.param