Hello and welcome to PP.
I am not familiar with parakeets so do not know if there are any 'rules' to keeping several birds in one cage if it is large enough that they all can have their own space. They seem to manage in the wild in huge flocks but maybe it is different in the confines of a house.
Are the fights aggressive or are they just establishing a pecking order? They may sort out who is in charge out of the cages eventually at which point they may choose to all live in the same cage.
I would leave the decision to them (with oversight to make sure all is cool).