Ever wondered why the Japanese prefer their cats with those funny tail-knobs instead of proper waving tails? I have an answer of sorts: folklore has it that if a cat was allowed to keep a long tail, reach a certain age, be kept for a certain number of years, or grow to a certain size, it might attain special powers and become a bake-neko, or monster cat.
That means Puddums will (according to Wikipedia's great article) haunt any household it is kept in, creating ghostly fireballs, menacing sleepers, walking on its hind legs, changing its shape into that of a human, and even devouring its own mistress in order to shapeshift and take her place. Which sounds pretty much like business as usual around here, but they can use their powers for good as well; both sides of the story here. The neko-mata is a related beast and one could make a case for the fabulous Catbus in My Neighbor Totoro as a kindly shapeshifting demon.