It's hard not to imagine that Daniel M. Pinkwater's classic "young adult" novel Alan Mendelsohn, the Boy from Mars (1979) wasn't heavily influenced by Robert Sheckley's Mindswap (1966).
Sheckley's novel involves a bizarre and disorienting trip across first planets, then the hero's hallucinations, and finally a "Twisted World" in which the laws of physics themselves are topsy-turvy; along the way, a sequence of intelligentsia and gurus mislead and confuse our befuddled hero. Pinkwater's novel involves first bizarre telekinetic experimentation, then interdimensional travel by intrepid highschoolers, all following the accidentally successful guidance of a weird guru named Samuel Klugarsh.
Sheckley's novel begins and ends with a character Kraggash, who steals our main character's body (inspiring a flight of his mind through a sequence of replacement bodies), and returns at the end, leading him into the Twisted World and a disorienting battle of wits.
Kraggash and Klugarsh are both mystical anarchists who lead our heroes through layers of self knowledge and surreal disorientation. The multiple worlds in Mindswap and multiple dimensions in Alan Mendelsohn play for very different effects, but they both combine the familiar with the alien in a manner sensitive to the inherently imagined and created aspects of our reality.
Not at all to belittle Pinkwater's novel, which, I think, over all is more effective and a greater achievement. (Though my long history with it perhaps biases me. . . )