This may be no more than a manifestation of Kato's preference for felines, but the cats in both CT and CC seem to hold a special place in the household.
If you look at the three most important families of both series: Crono's, Zeal, and Serge's you might notice something strange and recurrent. In each household the father has been lost, disposed, or possibly non-existent; we never see nor hear of Crono's father, King Zeal's disapearance is barely mentioned, and I think we all know the fate of Serge's father.
In each of these instances the father is gone, and what do we have but a cat taking up the space. Crono's cat seems to be of the regular household nature, but Janus' and Serge's are both a little different, the father is explicity identified with them. The name Alfador ("All-father", another name for Odin in Norse myth) seems to convey this rather strongly. And in Serge's case he knows the cat Lynx to be his own father, Wazuki.
This led me to conjecture--though not strongly at the moment--that maybe Alfador is King Zeal (this is partly inspired by AuraTwilight's comment in another post, though the cat thing has been bothering me for a while). Surely, it's not a far fetch to say that Queeny in all her Lavos-inspired might could replicate the side-show trickery of Sneff. But why would she do such a thing to her husband? To sush him up; to take the crown; to appease Lavos; any one of these could be true. Anyway, this is mostly hypothetical play, as we will never know.
This may have something to do with the status of cats in Egyptian myth, but then again, maybe Kato just doesn't like dogs.