Linnaeus answered that for you.
After the Felidae --- there's still a lot to go, but I doubt "flat-headed cat", "domestic cat" and "chinese mountain cat" will be used --- you go up the evolutionary tree to go to the Feliformae... Hyena's, Mongooses, and the like.
You see they've already been mixing the Pantheridae and Felinae freely, there's ocelots, margays, caracals, servals and clouded leopards etc still to go. Feliformae gives us binturongs, liksangs, civets, genets, ... . From there it's a small mental (but larger evolutionary) jump to the Mustelids --- the weasel family which I think is appropriate: small expensive sneaky critters that punch above their weight.