I would keep them together for short periods during the day when your home to monitor them and see if they are just having little tiff's or acutually fighting, I also have three and they like to go into the one big cage but they like to fight over the food dishes even though there is more then one
they will squawk at each other and push each other off but they get over it or if the squawking is to bad I usually remove one of them from the situation so far there has been no "real" fighting or blood shed there are alot of people that have 3 or more in cages together that get along fine but you also have to be careful because just like people some are just not meant to live together.
Do you have enough food dishes for all of them perches toys etc....
Do you have enough food dishes for all of them perches toys etc....