You can get more cats by trying out for adopts under the
main page. If a cat has "Adopt me" written on its page (i.e.
this cat), it is up for adoption. (Be sure to check the competition's end date, however, as some competitions might be over but still have the "Adopt me" sign up.) If you win the competition, you win the cat and can add them to your Clan!
You can also get more cats by submitting a custom form when an artist opens custom slots (they'll post on the main page), by breeding your cats in the
nursery (when an artist opens slots), or through finding them in
explore. If you have spare C$, you can buy a MYO (make your own) from the
MYO page and design a cat for yourself (or have someone else design it for you).
Hope this helps!