Coincidence? Of course not. Moreover, it turns out that six of them are...curled up! Now what is it that cats do more than anything excepting, perhaps, hedgehogs and armadillos? Of course! So here we have the explanations for the nine lives - three of them are curled up in the "extended" dimensions we can see, and the other six are curled up in the curled-up dimensions we can't see.
Wait, so all we really have to do to make the 6 "curled-up" dimensions detectable from our frame of reference is to strap a buttered croissant to a cat's back and drop it!
The multidimensional existence of all cats would instantly become perceptible. Lovecraft would be so proud.