It really depends on the species of the birds, the gender of the birds, and the size of your cage, plus some other facts. Some birds are more passive than others. Some other birds are born territorial and aggressive. Sometimes passive birds can become more aggressive when there isn't much space for everyone.
I have had trouble adding a new bird into my cage of two parakeets a little over two decades ago. The new bird was bullied immediately, but I can't blame the two older ones who were just annoyed because the new comer was jumping around like if his feather was on fire. I'd be annoyed too if there is a person running around like nuts in my room nonstop.
