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If you bring in another bird many avian veterinarians would recommend a 90-day quarantine period, or at the very least a quarantine minimum period of 30 days. The longer the quarantine the less likley an incubating disease will be spread to your current birds. A check up by an avian vet may also be a good choice for a new bird.If possible a bird kept in quarantine should be maintained on a separate air system apart from other birds but at the very least they should be in different rooms.
Quarantine time will give you a chance to work with your new bird and get him used to you etc. Wash hands between handling the different birds.To cage multiple birds together you will need a large cage when the time comes that you know the birds can get along from interacting out side their cages which can begin once you know that the new bird is not ill.
Signs of incompatibility between birds would include hissing, screaming, lunging, biting, tail bending, feather pulling, and other aggressive behaviors. Cockatiels that do not get along should be kept in separate cages and leave socializing between them to time spent outside the cage or interacting only from the safety of their individual cages.
Three may get along together, the new bird may bond with the female and want to drive away the other male, or they might none of them get along.
Hope this helps you!
There might be less of aproblem with two females and one male but nothing would keep the resident female from resenting a new member of the flock with similar results to having two males to one female. The bird that is left without a mate may attack the other birds or fight with the one of the same sex etc.
The problem is typically this species bonds in pairs so the 'odd one out' can have a difficult time depending on the personalities of the birds.
You can always try it as long as you are ready to do a seperate cage if needed.
But again quarantine to start with is important.