the thing is that they have to be a form changer, but you have to define what kind and when. Its easy give an idea, but its hard to get direction when you don't know where you want to go. Is this more of a theme change or a play style change? Does the change really do anything or not? Is this an ability change or a passive change?
When i think of multiple personalities I'm thinking in 2 ways either a passive change (changes forms due to a passive) or a theme change. I'll start with the theme change because its easier. It would simply be that after doing X the person changes forms, but doesn't really change. I'm thinking of Launch from the original Dragon Ball here. While Nice launch is well nice she is also timid, but it doesn't take away from what she can do. Then Rogue Launch is crazy, brash, aggressive, and unpredictable yet again they all do the same thing in terms of skill. This would be easier overall to implement, but a pain because now you are making 2 different models meaning twice as much work on skins. I would imagine the trigger here would be some form of CC or another like maybe only roots or only stuns causes her (been changing it but going to make this champ a girl) to change.
The second is a passive change. This would be something ultimately out of the players control that would force the change. I actually draw on TV and Movies for the visual, but that person who is maybe nice normally, but when put under extreme pressure or stress they let another personality out and become violent. This would work where after they reached a certain % health they would change forms and wouldn't change back until they reached a higher %. So they might change at 50% to the second form, but not change back until 65% (higher numbers and would need to be lower). Otherwise you could get stuck in a loop that would not be fun especially if they have different kits. Here I think the goal would be to have a weaker champ overall until they hit that %HP to change and then give them stat boots based on something geared in the passive to make them stronger overall. Mainly be more of an overall steroid. Think of like Ryu going evil Ryu or Goku compare to SSJ Goku. Thats the model this idea is based off of.
Hope that gives some direction overall as to how they will probably have to work to make it balance and be a true multiple personality