Oh my I certainly would NOT put them together in a cage, in fact, I'm not sure I'd even let them out of their separate cages at the same time. I do not believe plucking is a 'learned' behavior. Think of it like you would someone who self-mutiliates - like cuts himself. That is not learned, and neither is plucking - wild parrots never pluck, only birds in captivity. I cannot stress enough to keep them separate. They can be in the same room, even close by each other for company. Provide as much stimulation for the Eckkie as you can, like seed covered pinecones, wesco kabobs, treats wrapped in coffee filters that he has to figure out how to get to them, paper boxes with treats in them. Put all kinds of treats in a millet holder and suspend it where he has to work to get at it, with the millet on top - I'm talking like nutri-berries in there, and avi-cakes, things that are nutritious on their own.
The very first thing that should happen is the Eckkie taken to the vet to determine if the plucking is caused by a medical condition or allergy. I have a bird that had self-pucked himself for several years, and now he is fully feathered, but I think I was lucky, but I tried to give him everything to stimulate him including putting his cage beside some lovebirds for company. Please do not hestitate to ask for advice, and please keep us updated. Your screen name is 'teenagebirdmom' - so if you are a teenager you might want to consider whether you have the resources to provide for medical attention as well as a proper and healthy diet for this bird, or if in the best interests of the bird that you find him another home that is better equipped.
Plucking behaviors can be changed, but not always, and there are some very plucked birds out there that in fact are healthy but still pluck. Just be careful with the larger bird around the smaller. Even smaller birds can be a danger to larger ones - I have Pacific Parrotlets - they are tiny parrots, they kind of look like tiny Amazons, but nobody told THEM that they are tiny, and they act just as if they were as large as any other parrot and will go after far larger birds. Good luck here and think about what you can afford and what kind of time you have available. In another thread I see that you have just got yourself a conure as well, it is important that you don't overwhelm yourself and take care of what you already have before taking on new responsibilities. You certainly don't want to be a collector. Just be careful TBM, and don't bite off more than you can chew.