We had Charlie the cat from DD being 8 -24yrs old, so yes like you Swimmy we split the care.
As an adult I made clear her choice of a new pet was her responsibility financially ~food, insurance, jabs, feeding etc and it's worked out. It helps to agree who's responsible for what right from the start whether, child, teen or adult child. While that sounds obvious, clarity is everything.
I've had requests for a second cat. Nope. That's something for you to look forward to when you have your own home.
