1 Male and 2 Female

Well, I've never bred quakers, but I'll give you my thoughts.  I'm not clear on what it is you want to accomplish.  Are you concerned that the single female is lonely, or are you hoping they will all breed together?

The pair may feel bonded, even if they haven't started breeding, and putting another bird in the cage could be a danger to the new one.  It may also raise the stress levels and discourage breeding.  Quakers may breed in colonies in the wild, but they do breed in pairs and are not polygamists, and each pair has its own space.

Putting a new parrot into an occupied cage all at once should not be done in any case.  At a minimum, you should see how they interact together outside of their cages, and then slowly try to integrate them.  For breeding purposes I wouldn't even consider it.

I think you need to talk to other breeders or to an avian vet before you do anything with them.  There is a lot of experience on this board with parrots as companions, but I'm not aware of anyone who breeds them.