diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index bcebe3ab024ba..0556ed754af82 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -186,6 +186,38 @@ representation of :class:`DataFrame` objects (:issue:`4889`).
     df
     df.to_dict(orient='tight')
 
+.. _whatsnew_140.enhancements.shift:
+
+DataFrame.shift and Series.shift now accept an iterable for parameter ``'period'`` and new parameter ``'suffix'``
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The :meth:`DataFrame.shift` and :meth:`Series.shift` functions can take in an iterable, such as a list, for the period parameter. When an iterable is passed
+to either function it returns a :class:`DataFrame` object with all of the shifted rows or columns concatenated with one another.
+The function applies a shift designated by each element in the iterable. The resulting :class:`DataFrame` object's columns will retain the
+names from the :class:`DataFrame` object that called shift, but postfixed with <name>_<num>, where name is the original
+column name and num correlates to the current element of the period iterable. The function also now takes in a ``'suffix'`` parameter to add a custom suffix
+to the column names instead of adding the current element of the period iterable (:issue:`44424`).
+
+Usage within the :class:`DataFrame` class:
+
+.. ipython:: python
+
+    df = pd.DataFrame({
+        'a': [1, 2, 3],
+        'b': [4, 5, 6]
+    })
+    shifts = [0, 1, 2]
+    df.shift(shifts)
+
+Usage within the :class:`Series` class:
+
+.. ipython:: python
+
+    ser = pd.Series([1, 2, 3])
+    shifts = [0, 1, 2]
+
+    ser.shift(shifts)
+
 .. _whatsnew_140.enhancements.other:
 
 Other enhancements
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 8c85c4e961d99..ec1467f64e617 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5326,9 +5326,38 @@ def shift(
         freq: Frequency | None = None,
         axis: Axis = 0,
         fill_value=lib.no_default,
+        suffix=None,
     ) -> DataFrame:
         axis = self._get_axis_number(axis)
 
+        # GH#44424 Handle the case of multiple shifts
+        if is_list_like(periods):
+
+            new_df = DataFrame()
+
+            from pandas.core.reshape.concat import concat
+
+            new_df_list = []
+
+            for i in periods:
+                if not isinstance(i, int):
+                    raise TypeError(
+                        f"Value {i} in periods is not an integer, expected an integer"
+                    )
+
+                new_df_list.append(
+                    super()
+                    .shift(periods=i, freq=freq, axis=axis, fill_value=fill_value)
+                    .add_suffix(f"_{i}" if suffix is None else suffix)
+                )
+
+            new_df = concat(new_df_list, axis=1)
+
+            if new_df.empty:
+                return self
+
+            return new_df
+
         ncols = len(self.columns)
         if axis == 1 and periods != 0 and fill_value is lib.no_default and ncols > 0:
             # We will infer fill_value to match the closest column
diff --git a/pandas/core/series.py b/pandas/core/series.py
index ffa31b4f66211..309e7193afe6f 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -9,6 +9,7 @@
     TYPE_CHECKING,
     Any,
     Callable,
+    Collection,
     Hashable,
     Iterable,
     Literal,
@@ -4938,7 +4939,18 @@ def _replace_single(self, to_replace, method: str, inplace: bool, limit):
 
     # error: Cannot determine type of 'shift'
     @doc(NDFrame.shift, klass=_shared_doc_kwargs["klass"])  # type: ignore[has-type]
-    def shift(self, periods=1, freq=None, axis=0, fill_value=None) -> Series:
+    def shift(
+        self, periods: int | Collection[int] = 1, freq=None, axis=0, fill_value=None
+    ) -> Series | DataFrame:
+        # Handle the case of multiple shifts
+        if is_list_like(periods):
+            if len(periods) == 0:
+                return self
+
+            df = self.to_frame()
+
+            return df.shift(periods, freq=freq, axis=axis, fill_value=fill_value)
+
         return super().shift(
             periods=periods, freq=freq, axis=axis, fill_value=fill_value
         )
diff --git a/pandas/tests/frame/methods/test_shift.py b/pandas/tests/frame/methods/test_shift.py
index 9cd0b8bb5b315..0cb43ffefe5a8 100644
--- a/pandas/tests/frame/methods/test_shift.py
+++ b/pandas/tests/frame/methods/test_shift.py
@@ -429,3 +429,23 @@ def test_shift_axis1_categorical_columns(self):
             columns=ci,
         )
         tm.assert_frame_equal(result, expected)
+
+    def test_shift_with_iterable(self):
+        # GH#44424
+        data = {"a": [1, 2, 3], "b": [4, 5, 6]}
+        shifts = [0, 1, 2]
+
+        df = DataFrame(data)
+        shifted = df.shift(shifts)
+
+        expected = DataFrame(
+            {
+                "a_0": [1, 2, 3],
+                "b_0": [4, 5, 6],
+                "a_1": [np.NaN, 1.0, 2.0],
+                "b_1": [np.NaN, 4.0, 5.0],
+                "a_2": [np.NaN, np.NaN, 1.0],
+                "b_2": [np.NaN, np.NaN, 4.0],
+            }
+        )
+        tm.assert_frame_equal(expected, shifted)
diff --git a/pandas/tests/series/methods/test_shift.py b/pandas/tests/series/methods/test_shift.py
index 4fb378720d89d..4ceb2a569aa9e 100644
--- a/pandas/tests/series/methods/test_shift.py
+++ b/pandas/tests/series/methods/test_shift.py
@@ -14,6 +14,7 @@
     offsets,
 )
 import pandas._testing as tm
+from pandas.core.frame import DataFrame
 
 from pandas.tseries.offsets import BDay
 
@@ -376,3 +377,15 @@ def test_shift_non_writable_array(self, input_data, output_data):
         expected = Series(output_data, dtype="float64")
 
         tm.assert_series_equal(result, expected)
+
+    def test_shift_with_iterable(self):
+        # GH#44424
+        ser = Series([1, 2, 3])
+        shifts = [0, 1, 2]
+
+        shifted = ser.shift(shifts)
+        expected = DataFrame(
+            {"0_0": [1, 2, 3], "0_1": [np.NaN, 1.0, 2.0], "0_2": [np.NaN, np.NaN, 1.0]}
+        )
+
+        tm.assert_frame_equal(expected, shifted)