There are four costumes that can be enhanced. These costumes are the Basic Melee/Magic/Ranged/Healing costumes. They can be purchased with guild Prestige or Loyalty Tokens.
At purchase, the costumes are at the Basic Grade. Much like leveling a guild cloak, costumes use items called Synthium Stones to level up. When a costume can be upgraded to the next grade, it randomly chooses a stat or effect that is relevant to the kind of costume picked.
To level a costume, go into your Inventory and click on the "Regrade Item" button. Click on the tab tagged as "Synthesis" (the fourth tab on the window). Select a costume to put in the "Base Costume" slot, and two Synthium Stone materials in the next two.
If one does not wish to have a certain stat or buff, it can be randomly changed using a Serendipity Stone, available from the Login Badge workbench in Mirage Isle. A costume must be of the Arcane grade or higher to re-roll the stats.