Villainous Crush: Shriek has a crush on Dog. Strangely enough, Cat seems to be attracted to her.
A few episodes suggest that Dog reciprocates Shriek's crush. In one where they're all convinced that the apocalypse is coming, Shriek confesses to and kisses him, prompting Dog to go into Post-Kiss Catatonia with a big goofy grin on his face.
Even Evil Has Standards/Pet the CatDog: Seeing CatDog swarmed with psychotic fleas and the flea belt no longer being enough to help them is enough to convince him to give them a flea bath with no apparent ulterior motive.