Cats demonstrate Ne, Si, Ni, and Se personalities. (I think. How would you differentiate a Ni and a Si cat?)
At the very least, I can think of: curious, "smart" cat and sleepy cat. This is assuming they're roughly the same age, of course, since that should factor in to behaviour (again--I think. I'm not a cat expert).
Being that cats aren't highly social creatures like humans, they lack Rational elements.
Discuss. And no, I'm not insane.