diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 22f6659367683..26ae7904b66fc 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -819,6 +819,7 @@ Datetimelike
 - Bug in :func:`to_datetime` was throwing ``ValueError`` when parsing dates with ISO8601 format where some values were not zero-padded (:issue:`21422`)
 - Bug in :func:`to_datetime` was giving incorrect results when using ``format='%Y%m%d'`` and ``errors='ignore'`` (:issue:`26493`)
 - Bug in :func:`to_datetime` was failing to parse date strings ``'today'`` and ``'now'`` if ``format`` was not ISO8601 (:issue:`50359`)
+- Bug in :class:`RelativeDeltaOffset` which caused inconsistent behavior upon multiplying a :class:`DateOffset` (:issue:`47953`)
 -
 
 Timedelta
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 0bc9751694e9f..edb7e3cac8314 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -1229,12 +1229,7 @@ cdef class RelativeDeltaOffset(BaseOffset):
             else:
                 td_nano = Timedelta(0)
 
-            if self.n > 0:
-                for i in range(self.n):
-                    other = other + self._offset + td_nano
-            else:
-                for i in range(-self.n):
-                    other = other - self._offset - td_nano
+            other = other + ((self._offset + td_nano) * self.n)
 
             if tzinfo is not None and self._use_relativedelta:
                 # bring tz back from UTC calculation
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index 933723edd6e66..190ceaa80e976 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -33,6 +33,7 @@
 from pandas.errors import PerformanceWarning
 
 from pandas import (
+    DataFrame,
     DatetimeIndex,
     Series,
     date_range,
@@ -1061,6 +1062,38 @@ def test_construct_int_arg_no_kwargs_assumed_days(n):
     assert result == expected
 
 
+def test_offset_multiplication():
+    # GH#47953
+    mo1 = DateOffset(months=1)
+    mo2 = DateOffset(months=2)
+
+    startscalar = Timestamp("2020-01-30")
+    startarray = Series([Timestamp("2020-01-30")])
+
+    resultscalar1 = startscalar + (mo1 * 2)
+    resultscalar2 = startscalar + mo2
+    resultarray1 = startarray + (mo1 * 2)
+    resultarray2 = startarray + mo2
+
+    expectedscalar = Timestamp("2020-03-30")
+    expectedarray = Series([Timestamp("2020-03-30")])
+    assert resultscalar1 == expectedscalar
+    assert resultscalar2 == expectedscalar
+    tm.assert_series_equal(resultarray1, expectedarray)
+    tm.assert_series_equal(resultarray2, expectedarray)
+
+    df = DataFrame({"T": [Timestamp("2019-04-30")], "D": [DateOffset(months=1)]})
+    frameresult1 = df["T"] + 26 * df["D"]
+    df2 = DataFrame(
+        {
+            "T": [Timestamp("2019-04-30"), Timestamp("2019-04-30")],
+            "D": [DateOffset(months=1), DateOffset(months=1)],
+        }
+    )
+    frameresult2 = df2["T"] + 26 * df2["D"]
+    assert frameresult1[0] == frameresult2[0]
+
+
 @pytest.mark.parametrize(
     "offset, expected",
     [