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The breeds are budgies, cockatiel, quaker, african grey and cockatoo. They all have their own cages, but we would like to build a large aviary to incorporate all of them and give them more play and flight room.
I know budgies and cockatiel's are fine living together as i have a large aviary in my back garden with both species intermingled. I'm not sure about the other birds though. If you look on this african grey website you can find all you need to know about them, including: "While inter-species friendships with other parrots are uncommon with African Greys, they require socialization with other parrots of any species" - http://www.africancongogrey.com/ Also, I read here: http://www.quakerparrots.com/health/quaker-parrot-longevity/ that: "Quakers are very aggressive with other birds. Mine bit my parakeets toe off. I had the cages too close and the parakeet climbed over onto the quaker's cage."
As for the cockatoo, you'll have to be more precise on what type of cockatoo it is. If you have problems with putting certain breeds together then I suggest you do what we did which was make the aviary and then using wire [usually chicken wire] create sections within the aviary, this way all birds have enough room and won't disturb each other.
Good luck 
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