Gamemode: Ultimate Bravery
So some people may know of the Ultimate Bravery Website that has not been updated in forever. Those who don't, it will give you a random champion, random build, random summoners, random masterys, and random ability upgrade order. It's kind of a stupid thing to do but can be fun sometimes, when playing in a game and you are the only one doing this it isn't as fun. I have played 2 games with some friends where we would do this (in a custom) and it turned out to be pretty fun, but if there was some kind of actual restriction to it rather than trusting people to do so then it could be cool.
I think a game mode that is on Summoners Rift, that gives you a random champion that you own, with a random mastery page, random summoners, when you load into the game, only 6 items are given to you to buy from the shop, and it forces you to max certain abilities. I think it could be a silly/fun game mode to in with 9 other people who are stuck with some very off-meta build.