A game with the time travel self interaction and self saving mechanics of Super Time Force Ultra. Doesn't have to be a side scroller. Bonus points for getting multiplayer to work reasonably. I've been theorycrafting ways to do multiplayer like this for years (and ultimately most of it feels disjointed in theory so IDK). I've only seen one super low budget game using this mechanic (as a main game mechanic, not a side puzzle like the Ratchet and Clank time puzzles) and the reviews weren't great.
I've been considering mixing it with 5D Chess with Time Travel mechanics and Advance Wars gameplay as a proof of concept and see how far that gets me... But I don't have time or energy to work on it after work...