It can happen when one bird can already speak a human language.
If none of the birds can speak in the first place, usually it requires to keep only a single bird in order to train it to talk. In order to teach them to speak our language, to get their attention is the first step.  With multiple birds in the same captivity, it is hard to get their attention over to you when they already have companions of the same species. I guess once one or more birds have already learned to talk, you can let them to be your assistant coach for the rest of the birds. 
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