4v4v4
This gamemode wouldn't be a featured gamemode, rather an actual one that players can play all the time, other than the 4 existing gamemodes of League, one of which isn't played as often... You've proven you can throw 12 players into one setting with Hexakill. This gamemode will require a new map with three bases. The lanes could form a three pointed star, or a curved form of it, with jungle filling in the center and possibly outside the concave angles of the star. The objective could be...
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A simple destruction of the other two enemies' nexus, once one is destroyed spawning will end for that team.
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A king of the hill objective that requires teams to fight over an epic monster, one atop a "mountain" or otherwise in the center of the map. Albeit this monster would be stronger and larger than baron, dragon, or vilemaw, and would probably require a level 18 team fully built to take on. It could also harass lanes from atop its high perch in the middle of the map. Perhaps a lava monster, scorched earth Xerath's big daddy.
This gamemode could make people think about getting to level 18 first and making sure that the 8 other players don't steal up the epic monster first, or rather from the team that got it low. It also gives more possibility for featured game modes on a new map. I prefer the king of the hill option, because it lessens the fact that two teams could group up on one team to then duke it out themselves.
I also know that a lot of effort was put into refining Summoner's Rift, and I think that you could make an outstanding map for this gamemode, possibly called the "Magma Chamber" (totally not stolen or anything) or based in Ionia for some possible tropical shore settings.
Edit* I didn't completely check the boards for a similar idea, though the king of the hill idea still stands. I also wish for the third team to be green for a RGB setup.
Edit** I'm pretty sure the king of the hill option is the much better option because it can have many variables that can be implemented to counterbalance a snowballing team and a chance of 'Teaming up' on one team.