How do I make a mob transform/evolve into an evolution?

the only way i know, is to spawn a new entity in place of the old one, with the same yaw and pitch for seemless transition, then despawn the old one.  for transfering nbts and stuff, you can put a brain-like item in the entities inventory, that holds all of the nbt data etc, and transfer it to the new entities inventory, just make sure, to change all procedures interacting with the entities nbts to now target the items nbts instead. 

for the transfer process, you have to use a block like get nearest entity of type blank, as theres no innate way to target a newly summoned entity. you can however increase the accuracy, by giving all entities an attribute, that shows if they are newly summoned or not, by having the default be 0, and changing it to 1 a second after spawning. so you can prevent getting the wrong entity, if it evolves surrounded by other entities. 

hope this helps.