diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index c12208db983e2..b3b9e53f48271 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -77,6 +77,7 @@
     ABCIndexClass,
     ABCMultiIndex,
     ABCSeries,
+    ABCSparseDataFrame,
 )
 from pandas.core.dtypes.missing import isna, notna
 
@@ -5334,6 +5335,15 @@ def _combine_frame(self, other, func, fill_value=None, level=None):
             #  overhead if possible by doing this check once
             _arith_op = func
 
+        elif isinstance(self, ABCSparseDataFrame):
+
+            def _arith_op(left, right):
+                # wrap the non-sparse case below with to_dense and to_sparse
+                dleft = left.to_dense()
+                dright = right.to_dense()
+                result = dleft._binop(dright, func, fill_value=fill_value)
+                return result.to_sparse(fill_value=left.fill_value)
+
         else:
 
             def _arith_op(left, right):
@@ -5356,7 +5366,11 @@ def _combine_match_index(self, other, func, level=None):
         left, right = self.align(other, join="outer", axis=0, level=level, copy=False)
         # at this point we have `left.index.equals(right.index)`
 
-        if left._is_mixed_type or right._is_mixed_type:
+        if (
+            left._is_mixed_type
+            or right._is_mixed_type
+            or isinstance(self, ABCSparseDataFrame)
+        ):
             # operate column-wise; avoid costly object-casting in `.values`
             new_data = ops.dispatch_to_series(left, right, func)
         else:
diff --git a/pandas/core/sparse/frame.py b/pandas/core/sparse/frame.py
index aaa99839144b4..a6d15ab4e2d4b 100644
--- a/pandas/core/sparse/frame.py
+++ b/pandas/core/sparse/frame.py
@@ -533,57 +533,10 @@ def _set_value(self, index, col, value, takeable=False):
     # ----------------------------------------------------------------------
     # Arithmetic-related methods
 
-    def _combine_frame(self, other, func, fill_value=None, level=None):
-        this, other = self.align(other, join="outer", level=level, copy=False)
+    def align(self, other, *args, **kwargs):
+        this, other = super().align(other, *args, **kwargs)
         this._default_fill_value = self._default_fill_value
-
-        new_data = {}
-        if fill_value is not None:
-            # TODO: be a bit more intelligent here
-            for col in this.columns:
-                if col in this and col in other:
-                    dleft = this[col].to_dense()
-                    dright = other[col].to_dense()
-                    result = dleft._binop(dright, func, fill_value=fill_value)
-                    result = result.to_sparse(fill_value=this[col].fill_value)
-                    new_data[col] = result
-        else:
-
-            for col in this.columns:
-                if col in this and col in other:
-                    new_data[col] = func(this[col], other[col])
-
-        return this._construct_result(other, new_data, func)
-
-    def _combine_match_index(self, other, func, level=None):
-        this, other = self.align(other, join="outer", axis=0, level=level, copy=False)
-        this._default_fill_value = self._default_fill_value
-
-        new_data = {}
-        for col in this.columns:
-            new_data[col] = func(this[col], other)
-
-        return this._construct_result(other, new_data, func)
-
-    def _combine_match_columns(self, other, func, level=None):
-        # patched version of DataFrame._combine_match_columns to account for
-        # NumPy circumventing __rsub__ with float64 types, e.g.: 3.0 - series,
-        # where 3.0 is numpy.float64 and series is a SparseSeries. Still
-        # possible for this to happen, which is bothersome
-
-        left, right = self.align(other, join="outer", axis=1, level=level, copy=False)
-        assert left.columns.equals(right.index)
-        left._default_fill_value = self._default_fill_value
-
-        new_data = {}
-        for col in left.columns:
-            new_data[col] = func(left[col], right[col])
-
-        # TODO: using this changed some behavior, see GH#28025
-        return left._construct_result(other, new_data, func)
-
-    def _combine_const(self, other, func):
-        return self._apply_columns(lambda x: func(x, other))
+        return this, other
 
     def _construct_result(self, other, result, func):
         """
@@ -639,7 +592,8 @@ def _get_op_result_fill_value(self, other, func):
             fill_value = self.default_fill_value
 
         else:
-            raise NotImplementedError(type(other))
+            # reached via _combine_const
+            fill_value = self.default_fill_value
 
         return fill_value