diff --git a/dask_expr/_expr.py b/dask_expr/_expr.py
index c00106ba..d014d806 100644
--- a/dask_expr/_expr.py
+++ b/dask_expr/_expr.py
@@ -1093,7 +1093,19 @@ def _task(self, index: int):
         return self.value
 
 
-class Blockwise(Expr):
+class BlockwiseOverlapping(Expr):
+    """Super class that operates like a blockwise op
+
+    We require information from neighboring partitions, so we can't prune partitions
+    before lowering, but the spec is the same as for Blockwise ops, we don't reoder
+    things, alignment stays consistent, ...
+
+    """
+
+    pass
+
+
+class Blockwise(BlockwiseOverlapping):
     """Super-class for block-wise operations
 
     This is fairly generic, and includes definitions for `_meta`, `divisions`,
@@ -1276,7 +1288,7 @@ def _task(self, index: int):
             )
 
 
-class MapOverlap(MapPartitions):
+class MapOverlap(BlockwiseOverlapping):
     _parameters = [
         "frame",
         "func",
@@ -1296,6 +1308,29 @@ class MapOverlap(MapPartitions):
         "clear_divisions": False,
     }
 
+    def _broadcast_dep(self, dep: Expr):
+        return dep.npartitions == 1
+
+    @property
+    def args(self):
+        return [self.frame] + self.operands[len(self._parameters) :]
+
+    def _divisions(self):
+        # Unknown divisions
+        if self.clear_divisions:
+            return (None,) * (self.frame.npartitions + 1)
+
+        # (Possibly) known divisions
+        dfs = [arg for arg in self.args if isinstance(arg, Expr)]
+        return _get_divisions_map_partitions(
+            True,  # Partitions must already be "aligned"
+            self.transform_divisions,
+            dfs,
+            self.func,
+            self.args,
+            self.kwargs,
+        )
+
     @functools.cached_property
     def _kwargs(self) -> dict:
         kwargs = self.kwargs
@@ -2454,7 +2489,7 @@ def non_blockwise_ancestors(expr):
         e = stack.pop()
         if isinstance(e, IO):
             yield e
-        elif isinstance(e, Blockwise):
+        elif isinstance(e, BlockwiseOverlapping):
             dependencies = e.dependencies()
             stack.extend([expr for expr in dependencies if not is_broadcastable(expr)])
         else: