After crossing dogs, you always get a puppy of the same rank as the parents. To try your luck and get a higher level dog, you need to raise the puppy. Only after that, the new animal will either receive a higher rank or not. For example, when crossing two dogs of rank 1, you can get a rank 2 dog, or, if you are less lucky, a rank 1 again. Certain skills of your character and other dogs can increase the chances of success!