Is it possible to play a class/race card on another player with their permission?

[Pleh]

Of course, there's nothing preventing you from making a deal to have the same effect. If "Bob" is the lowest level person in the party, you could both agree that on your Charity phase you'll give him a Dwarf card (which then he could legally play on himself immediately since he had just received the card) and in exchange he would give you the boots. The only caution I would take care to emphasize is that such deals are not binding on players and there is a risk of one munchkin or the other not keeping their end of the bargain.