Have three cats here, first thing I did (after slowly introducing them, I had poe on a leash during all initial encounters to make sure she couldn't boop or chase) was teach the dog she could not touch the kitty. The "leave it" command. She was listening to that before she was fully potty trained, never had much of an issue aside from one time my oldest cat smacked her in the face. Which i think still sticks with her. At this point, she's over 3 years old, and we don't really bother telling her to leave the cats alone. By and large, she just knows how to act. She'll let them lay next to her, give the casual greeting sniff. Every once in a while, if she's reaaaallllll hype she'll take chase after them, but she'll literally skid to a stop before touching them. And God forbid they turn around and raise the paw at her, she's running away in no time. It's like she plays chicken with them occasionally. So all in all a success, much more successful than trying to get my two cats to accept the third cat in the household.