Actually, I suppose that's the point where even I had to admit I was out of control. At least mine came from my own pair (how can Amazons be endangered when they breed like rabbits?) You're probably still in a safe place with "just" three, but any more would probably be pushing it.
Thankfully, I'm down to one at last. I can attest to the fact that the more birds you have, the less you can interact with them. Actually, more than one and they really don't need you. I had started out with one Orange Wing and got stupid and thought he needed a friend for company because I wasn't around all the time. As soon as I introduced her, my sweet baby didn't need me and the PITA really started. Instead of buying a 5# bag of food once a month, I was buying at least 25, and going through as much veg as the rest of the family eats. The seed hulls and feathers were impossible to keep up with. Tried to corral them into one room so I could at least close off the mess periodically and all that meant was my FL room became a chicken coop (and this is FL--meaning we developed a roach problem. . .) and all the birds got neglected since they weren't in the hub of family activity.
My little guy (the first surviving offspring) prefers to have the limelight and would probably prefer the cats and dog were not here, as well. It is so easy to succumb to "just one more," but that will not be a mistake I make again. It doesn't take too much to lose control and really, once you get too many you're just warehousing animals and not integrating them as members of the family.
I had the same problem with babies, FWIW--always had that overwhelming urge to have "just one more" to fill my arms once the last one got independent on me. Thankfully, I stopped at two and have finally reached the point where the hormones are abating and I can appreciate how insane it would have been to indulge my urges. Unfortunately, there is nothing like menopause to render me less susceptible to furred or feathered babies. That's just got to be willpower. My pristine, remodeled FL room is a good reminder not to let myself go apeshit again. :P