Your placement of this thread in the "Cages" sub-forum poses an interesting question. Was it placed here because you wish to know whether your potential parakeet can be housed in the same cage as your conure? If so, I would advise against it, since many conures are known to be rather territorial and can become aggressive. Housing two parrots together in the same cage sometimes does work - I have a budgie and cockatiel sharing one right now, although it must be said that they are rarely locked in together and neither of them are particularly territorial so in their case it works. My lorikeet on the other hand is HUGELY territorial and prone to bouts of extreme aggression and simply cannot share a cage with anyone. Your birds may get on just fine outside their cages in neutral territory, but I think it's best if you arrange for your new addition to have it's own living quarters, for safety's sake
I have never had close contact with either species, but someone told me red rumped parakeet are extremely territorial. That person compared them with the same level of territoriality of the pacific parrotlet (which I know well) and I would say that must be a good amount of aggressiveness.
Moreover, if the cage is small, I always think there is some risk or disease transmission as microorganisms that are not harmful for one species, might be to the other.