If James is the hero of Catskinner's Book, Catskinner is the anti-hero.
He starts out a monster, and by the end...he's still a blood-thirsty monster. The only real change is that James has increased his mastery and control over Catskinner. In the initial explanation of the strange relationship between man and monster, James tells us that Catskinner called all the shots during his childhood.
It's worth mentioning that I'm not sure if Catskinner's early days pinned to in James' back by a magic tattoo count as a childhood, given the implication that Catskinner is old as we reckon things, and a creature for whom time his meaningless as he reckons things. His early behavior, unchecked and impulsive, is a childhood of a sort. It's not until James becomes old enough to threaten Catskinner with punishment that Catskinner reins in his murderous ways.
The 'character building' that Catskinner goes through in Catskinner's Book amounts to little more than surrendering control to James on a more regular basis, and doing a much better job of keeping James as healthy from a mental standpoint as from a physical one. Does surrendering control to somebody who exercises more and more control over your behavior counts as growth?
Perhaps, if you're talking about a manchild who settles down and sacrifices more and more for his family. If you're talking about a selfish Scrooge who learns to use his wealth and power to care for others. And maybe it even counts for demonic beings of pure thought and malice from another universe who learn to kill only those who deserve death, and who learn to allow their host critter to experience a little hanky-panky once in a while.