So I got this idea from the quiz site, Sporcle. In it, players had to click on an equine, feline, canine, feline. 
For example: zebra, tiger, wolf, persian until the options were used up.

I decided to bring it here, but altered for forum use.

I will name an equine. Player 2 will name a feline. 3 will name a canine and 4 will name a feline. And so on.

Acceptable: breeds, species, mythical (not one you made yourself).

SHIRE

Marwari

Bobcat

Corgi

Manx

Tennessee Walker

Oriental

Timber Wolf

Ragdoll

Mustang

Siamese

Maltese

Pallas cat

Brumby

Tiger

South American Chilla

Sand Cat

Quarter Pony

Cornish Rex

Staffordshire Terrier (:

cheetah