As others have said, when you're getting your next classes you'll have to progress by killing monsters instead of doing quests. Whether it's hunt logs, leves (which honestly you should save for your Crafting profession seeing as they're more limited in their leveling options at least early on), guildhests, or FATEs you should have plenty of options.

On top of that though you also get a bonus to your experience gain based on the level differences between your classes.