Actually, this would only make sense from a lore perspective if all races were open to all species. Werewolfism is a different strain from weretigerism.
If a khajiit is bitten by a werewolf it turns into a werewolf. If it's bitten by a weretiger it turns into a weretiger.
If an Argonian is bitten by a weretiger it turns into a weretiger.
If a human is bitten by a were-crocodile it turns into a were-crocodile.
Else humans would be turning into were-apes.
I think it could happen if it was unlocked from the Crown Store as an option. A monetary thing, I'm sure it'd be a popular purchase. I'd totally give my khajiit a weretiger strain of lycanthropy.