Cats are nothing more than a macroscopic collection of interacting quantum systems (or particles). However, cats have developed a rather fine degree of control over the probabilities of their various superposed states.
Take for example the above post by MLS about the cat that suddenly appeared. Actually, that is just a quantum tunneling effect that could happen to any cat, any time, anywhere, but only with (normally) very low probability. What the cat seems able to do is alter the probability density functions to make this much more probable, and therefore it will actually happen more often.
The other posts in this thread are similar. The one about the cat that jumps into the tub with water then jumps out with only the bottoms of its feet wet can also be explained straightforwardly as a sequence of quantum events, over which the cat can exercise some control.
Bear in mind, of course, that for each of these observations, there suddenly springs into existence a collection of alternate universes, in each one of which a different one of the possible outcomes has happened.
My neighbor is building a cage of chicken wire on a wooden scaffolding to put over his plantings to keep the cats out. But that will be an easy one for the cats to defeat. Cats will have no trouble at all quantum tunneling right through a mere sheet of chicken wire.