You mean like cats? (That's not a rhetorical question, by the way. When you domesticate tigers, would they be very different from what we now consider a cat?)
That's sort of the process we had to get the bengal (hybrid asian leopard cat and housecat), which is considered a domestic cat after 4 generations.
Same thing has been done with servals ("savannah cat"); I can only imagine how awesome/terrifying it would be with other lesser wild cats, although I think there are enough differences between the great cats and domestic cats to make it difficult/impossible to do naturally (tiger/cat or leopard/cat cross).
Didn't Siegfried and Roy hack the maternal instinct of female cats to achieve some semblance of domestication? I mean, it didn't work out very well of course, because a cat mauled Roy and nearly killed him by grabbing him by the neck (to drag him to safety, according to them) like she would a cub.
So, I think there is a hook. It's just a really shitty one. Note that the hook for dogs can backfire as well, if they try to assert pack dominance vs. their owner. So we breed really submissive dogs.