Sometimes they do and sometimes not. Parrots are like people in that they don't like all other birds.
Keep your birds in separate cages and allow supervised play time on top of cages until you see everyone getting along. When I say supervised, I mean you or another human is right there making sure there is no fighting.
Also, a cage that is large enough for two birds will not be large enough for three.Overcrowding will cause fights to the death. Each bird needs their own food and water dishes and plenty of room to fully extend wings without hitting anything or anyone in cage.
I recommend separate cages to make sure everyone stays in good shape.