"While Encyclopedia Britannica only lists fifteen cat breeds, The International Cat Association, the world's largest genetic registry of pedigreed cats, recognizes seventy-three different kinds." (Source)
"Selective cat breeding has historically been focused on aesthetic features (coat color, coat texture, and other traits defined by a single gene variant), rather than genetically complex body structure or functional/behavioral traits (as is the case in dog breeding). This has resulted in some cat breeds being defined by a single gene variant (responsible for a curly coat, for example) while sharing a multitude of other variants associated with common life history and geographic origin with other, visually different cat breeds." (Source)
Here are some candidates.