Well, I'm no bird expert...but as you know we have a GCC. Love him to pieces!!!
He has his own cage, but has supervised turn out time with our tiels. I have a huge cage that now houses our pigeon...but it came with the two tiels I rescued and at one time, thought that all our birds could live happily together with all that room.
Not the case...Franklin, although good most of the time, is quite a bully bird and I wouldn't trust him with another unsupervised.
Granted, every bird is his/her own personality...but if you do decide on another...you just might want a back up plan just incase your Con or your new GCC decided they aren't each other's cup of tea.
Also, as you know...we have 4 cockatiels...Chicken Little formed an extremely strong bond with our Charlie, so much so, that Chicken who is normally a very very sweet boy, becomes a vicious monster toward me when he's with Charlie. None the less, at times, I let the two of them hang out together. Never had a problem.
Yesterday, I had all the birds out, Chicken and Charlie are of course inseparable. I had to go back to work, put everyone away and decided to leave Chicken Little with Charlie happily snuggled up to each other and came home to find a HUGE amount of feathers in the bottom of Charlies cage. Both birds appeared fine...but what the heck???
When I got Chicken Little out to spend time with him and put him back in his own cage...to my shock...I found his back was nearly bald! His wings were covering his back where all his feathers had been plucked out.
Obviously in the 2 hours I was gone, there was a problem between them. So now, I won't be letting them stay together, unsupervised.
Our hens are housed together, and they get along great, so far, not a problem. You just never know...so I kindly advise you to have a back up plan incase your plan is kaboshed by your birds plan
Toni