I haven't messed around too much with RPG maker-type programs, so my knowledge on the specifics of it may be off. But if I'm understanding it correctly, then so long as the status/class is modified to match, then it should carry over, no? The character's HP and MP values are maintained, in theory you could make it so either EXP is a global value that is saved rather than a character-specific one, a temporary/current EXP value that is copied and pasted over between class shifts, or that personal EXP values carry over into new "classes." Or, heck, maybe make it so each form *has* to be leveled up individually, though perhaps at an accelerated rate to the player's current level. As far as abilities are concerned, you could either make them globally available in all "classes" the character can become and just fail if not in the right form, or unlock them for specific class(es) when used/when in inventory and therefore only appear with the applicable form.
Again, I don't have too much knowledge about how the coding of it works, but I think there would be ways around it.