Caress Love ( or idk, my english sucks, so ...) would be a new combat move, discovered once you tether your first animal, that can be used to, indeed, tame animals.
It should increase your openings for each colours and give a bunch of IP to the animal, but a chance to make him going out of combat, once beated well first of course

Pretty sure that Jorb could end up with a better mechanics, but well, Caress love still is the idea. ... feel free to speculate about how that should work.