I think it would be kinda cool if for a new champion (as a passive) or something they're allowed to level up past 18. Maybe cap at 20? and they get added effects because of it.
Nothing screams "late game" like being a higher level than all members on both teams.
(Edit: Then they'd have 2 extra points to spend on Q,W,E or R! Which players could decide on based on their situation?)