Witness one of my cats, who is very social and really likes company, plopping himself down during the middle of game map and materials during a recent Call of Cthulhu scenario.
This does disrupt the immersion a bit, but perhaps I’ll run a game sometime with a cat kaiju and thus have a ready-made NPC helper.
(We have two cats, but the other is a bit of a ‘fraidy cat. Thus, he does not interfere as much as this one who has made himself a player favorite.)