Think of Levemetes as daily quests on an 11-hour timer, instead of a 24-hour timer. That's pretty cool, don't you think?.

Happily, there are still ways to gain enhanced XP when you have hit your Levemete cap:

Look for FATES and jump in;they seem to pop up pretty regularly.

If you qualify for dungeons, run them, too. As far as I know there is no daily cap on running dungeons, so you can do them as often as you like.