Many of my guests at games are cat people and DS9 fans (as are my wife and myself). In the episode "Honor Among Thieves," Miles O'Brien adopts Liam Bilby's cat, Chester. He is seen bonding with Chester at the end of the episode.
I imagine this is a low priority, as it should be, but Spot has a card, and it would be great if Chester had one too. All those Reshape the Quadrant decks would be that much more fun if we could stick a cat in them.
I am hesitant to make any specific suggestions for the stats/skills/game text of Chester's card, because I understand maintaining a delicate balance is very important for tournaments and whatnot (about which I am not qualified to comment), but it would be cool for Spot to have a pal. Or a mortal enemy, knowing cats (our dainty princess tried to kill my cousin's large but gentle and quite terrified tomcat on sight when we were cat-sitting; had to keep them in separate rooms).
It would also be awesome to have a bunch of cats in the game with their own mechanics, but I'm not sure that could fit into a Star Trek game, considering that we only saw two cats on screen (though the Enterprise-D had 12 male cats on board according to Data, if I recall correctly), and I highly doubt the committee would consider such an addition worth their time, and I wouldn't blame them.
The same treatment could be given to dogs (out of fairness), but I'm not really a dog person so I can't write intelligently about that. I love other people's dogs, but I'd rather not have one in my house.