Regulus getting injured and instinctively going to Sirius, except he panics and becomes Animagulus last second so Sirius opens the door and this tiny kitty is here. Maybe he's never been a big cat person, but he's sure Remus would know how to heal the cat.
Remus and Sirius adoringly take care of this fluffy cat and Regulus kind of likes being taken care of. The other half of him is probably thinking about how undignified it is.
Shenanigans ensue, Regulus transforms right in front of them and Sirius realizes that the slightly pompous look on the cat's face makes a lot of sense. He doesn't kick Regulus out since he clearly enjoys living in the house enough to not run away.
I bet Regulus the Cat could comfortably sit on Moony's back and it's kind of funny because just imagine a tiny void on this massive wolf. Reggie would fucking vanish if he was sitting on Padfoot and that's very funny to me