A champion that breaks the level cap?

A common trend in games with mulitple pieces is to have a character or element that "breaks the rules." A couple of examples in League are Karma, who starts with her Ult already learned, and Jayce, who gets 6 points for each ability but lacks an ult proper.

What about a character that can go past the level 18 cap, with all the scalings per level that that entails -- stats gained, damage increases on certain item actives or runes, and, particularly, an extra point for each ability (up to level 22)?

What kind of character design would fit best for this kind of mechanic? I was thinking a Mage makes the most sense, the type that pursues and peruses knowledge, but haven't given it any more thought beyond that. I just think it would be neat to see a champion with a hyper late game that isn't built around a minigame like collecting chimes or stacking one ability.