Do you think the newest pets of the humans could diverge and form their own new species solely formed to our behavior and needs like dogs?

Lets say the parrot and other high iq birds, could the pet form have different behavior social wise and or change in their bodies?
The dogs that could make a pouch face got more sympathy from humans, could parrots also evolve these things to be more acceptable to humans?
I am retard and this question might be full of shit but i realy wonder this pic unrelated