Great This is a very good move, and I look forward to seeing whatever you come up with.

Assuming by "not looking at multiplayer" you specifically mean network/online multiplayer, here's my idea:

I vaguely remember a long time ago playing a simple 2D shared-screen multiplayer game. It was viewed from side-on, but I wouldn't call it a "side-scroller" simply because the entire level fit within the view, so there was no "scrolling" to be had.

The premise is simple and based on how Nintendo's Mario defeats his enemies: jump on your opponent's head. This was a multiplayer game (no online -- just shared keyboard, or one player on mouse, or players using gamepads) in a small platform-style level where you are trying to jump on each other's heads. It was really chaotic, and a lot of fun if I remember correctly. Jumping on an enemy's head would explode them in a shower of bodily organs as the jumping player bounces high into the air.

For your version, there's no reason it couldn't be 3D models, animations, shaders and so on a la Little Big Planet. You could also add bots relatively simply. You could start extremely simple (run, jump, explode in a shower of vitals), and fairly easily add more layers of controlling depth (wall-jump, roll-dodge) without making it too complex for two players to play on one keyboard. You could also add bots and environmental hazards (I think the one I played had spikes) and other environmental factors (I think the one I played had slippery ice and water you could swim in).

If anyone can remember the name of this game, I'd love to know. I haven't been able to find it.