I recently had an idea for a new system that replaces crit at leage of legends and a rework to an old system which would replace dodge then. The 2 things which I would suggest are:
% increased damage
This works actually like the stat crit dmg, but not random. Some abilities like Poppy's Diplomatic Immunity already feature that. It should be perfect, because it is counterable, not like true dmg, but not RNG. If you get items which increase that, you no longer need crit at all. Ashe's Focus could increase the % increased damage for the next hit. Or Tryndamere's fury bar could increase damage depending on fury.
This should maybe cap at 300% bonus damage, otherwise, some champs could be OP.
% Armor and magic resist increase
This would be the direct counterpart to the % increased damage. Increasing armor and magicresist means the enemy has to get more armorpen and magicpen, making the increased damage countered. But, it shouldn't be too high.
But, Magicresist and Armor should also cap now, maybe at 400.