I don’t believe we have a Cheshire Cat in Pathfinder yet, but the pard isn’t a bad start. Like many other magical beasts, its party trick is phasing…but unlike other magical beasts, it can scorch you as it runs through you. (Think the X-Men’s Kitty Pryde, a.k.a. Shadowcat…if she were on fire.)
Pards are too smart to serve as ranger companions without the help of some feats or a kind DM, but well-role-played PCs could certainly ally with them if they can work with the cats’ empathic communication style.
Said empathy and phasing, by the way, opens up whole other questions… Are pards simply the magical beasts one would expect in a magical world? Do they come from the lands of the fey (as their diet suggests) or the Ethereal Plane (like phase spiders)? Or is the “alien” adjective in Bestiary 4 used literally? Could these be cats from another planet? Or felines from whatever reality aeons hail from, where symbols and metaphor trump words every time...?
Quicklings in a drought-stricken forest approach a party of adventurers asking for aid against a den of pards. This leaves the adventurers in a quandary: Can they refuse fey asking for help, even evil ones? Even if they feel they can, the pards are also decimating grig populations in the area. Worse yet, the cats’ scorching phase attacks, normally only a danger to their prey, risk setting the entire woods aflame.
An android wishes to learn emotions. An encounter with a pard left her enamored with the creatures, and she followed a pard den through five seasons learning to communicate with them, albeit roughly. The android now has a pard companion who is fiercely protective of her—it regards her emotionless default state as it might an infirmity in its mate or child—and she in turn will swear everlasting vengeance on anyone who harms her pard…which, for an android, can be a long time indeed.
In the City of Golden Towers, discontent is roiling the mamluk class. Long the sultan’s elite troops and bodyguards, they are finding more and more of their traditional functions being handed to the Red Sashes. This order of monks and shadowdancing janissaries from the mountains is resented for offenses large and small, from usurping the mamluks’ power to dietary differences and declining to wear the traditional purple turban. Adventurers are asked (or coerced) by mamluk representatives to dig up dirt on the Red Sashes. If they are caught they will have to face not only the warrior monks, but also the trained pards that are the order’s mascots and hunting companions.
—Pathfinder Bestiary 4 211
Edit: Thanks for your patience with this post. Original entry: Can't talk. Wilco-ing. Psychedelic cats can wait. Thanks for understanding.