Have the cat do the same thing repetitively - It walks 10', turns left, sniffs the ground, meows, walks 10' back, licks it front paws for a minute, repeat. This could be an association with a geas that missed a targetted character. Or the cat is actually a physical representation of a ghost/poltergeist that is nearby. If the characters decide to move it, attack it, whatever, it still does the same thing, but as soon as they leave the room or take their eyes off of it for a bit, it comes back. If they complete a certain task related to the cat, then the cat-ghost could appear to be put to rest - "ROARAAWWLLL!!!!!" And have them do the same thing 9 times, fight included.