Rollcage: Stage II did quite a few things right. One of those things was Demolition mode.
You fight your local co-op partner over who can destroy the most destructible objects in a track (of which there are a lot in Stage II).
Buildings are worth 2000 points, rocks/trees/flares/lamp posts/fences and everything else is worth 200 points.
You can select an amount of time to gather points in, or even set it to end only after all objects are destroyed.
GRIP doesn't have any destructible objects right now, but if those are ever properly implemented, I feel like this mode would be a great addition for local/online multiplayer.
It'd probably need dedicated maps for it though, considering tracks in GRIP are quite a bit bigger than Stage II's.