So, I've reached the point where my village is pretty full until my kittens finally grow up, so I'm wondering now if Nestor can still show you a cat when your village is full and you can then make room and grab the cat later (but same day of course)? Or does Nestor not have the option at all to show you a cat if you have no open slots?
Thank you!

@Rapirisu yes he keeps showing you cats! you can just navigate away from the page, send a cat travelling and come back to pick up the new one

(same with starting a family prompts - they keep showing up, you just have to make room before you can accept)

Thank you for the quick response, the family part is also very good to know!