CatDog can be half cat and half dog, but you assume they would be a completely unique device. Instead of falling within either a dog or cat designation, CatDog should be its own creature. But that may not be quite the case.
In season 2’s “Sneezie Dog”, the dog develops allergies, believing that Cat is causing them. At the end of the episode, we find out that he is actually allergic to Winslow, but that brings up an important point. Dog was the one who had a runny nose throughout the episode, while Cat was perfectly healthy. This episode suggests that even though the two have the same body, they have separate immune systems. If true, it would result in many medical challenges.
Another example of this can be found when dogs eat several pecan pies and develop pecanitis in season 1’s “Dog’s Strange Condition.” Again, only Dog is affected, though Cat grows a tree out of his head at the end of the episode. It is a strange event because the symptoms should have affected them alike, but it suggests that their bodies are completely separate entities from each other. It is a dangerous situation for the two because one of their immune system could easily detect the other as a threat. That’s what’s going on below transplant rejection for humans when foreign tissues or organs enter a body that cannot medically accept them.
For all we know, CatDog’s body could slowly try to kill the “alien” device, and that brings up the most troubling question of all. If one dies, would the other also be forced to pull around the body until it also goes away? On second thought, it might be best not to think too deeply about all of this.