That would probably be impossible, keeping track of 20 people in the same game.
What I'm suggesting is a community-run event, either just for the hell of it, or for a small prize or something mentioned in the lore, idk. I'm not talking about a 1-day event, this would be played out over the course of about a month, and it would operate like the board game RISK, if you've ever played it.
I do however like the 'different gameplay' type of thing you're thinking of though. I would have 5 teams of 2, with respawning nexuses, 2 or 3 turrets for each base, no inhibitors, no super minions. Get points for dealing the most damage to enemy nexuses (to prevent KS'ing nexuses). But that's a different department altogether =-)