I’m not sure how this would be a solution to rehoming a bird, unless you are out of town or out of the country regularly. In a case like that, birds can do fine staying with a friend from time to time. Parrots prefer a stable environment, and it is not their nature to be close with more than one person once they are mature. It depends on the bird. So changing homes on a regular basis may or may not work. All you can do it try it out and see how the bird reacts. If he grieves for the other person each time he is moved, this is not particularly healthy and could lead to serious behavioral problems or something like feather destructive behavior.
Thank you for asking Lafeber,