Theorizing that one could travel to parallel tooniverses where one's own species was sapient, Dr. Horace Horsecollar stepped into the Quantum Schlep accelerator...and vanished.
He woke to find himself trapped in one cartoon realm after another, facing equine mirror images that were not his own, and driven by an unknown force to change the overall cosmos for the better. His only guide on this journey is Mickey, an observer from his own tooniverse, who appears in the form of a hologram that only Horace can see and hear.
And so Dr. Horsecollar finds himself schleping from life to life, striving to put right what could go wrong, and hoping each time that his next schlep will be the schlep home.
This one isn't, though. This one has him schlepping into Big Mac's body just before "Applebuck Season."
And while this is definitely an entry in Estee's "Who Crossed Over My Little Pony?" contest in which it gained an Honorable Mention, it also might have something to do with this little TV series from the early 1990s called Quantum Leap...