When using Super Munchkin, can you discard one of your Classes and replace it with another, or just not replace it?

You can turn from, e.g., a Super Cleric-Wizard into a Super Cleric, or, if you have the Thief card, Cleric-Thief. This doesn't make you lose Super Munchkin. You cannot have a "naked" Super Munchkin card in play, even briefly.