If you try to equip an outfit which includes an off-hand item while wielding a 2-handed weapon, you get the following message:
If you are wearing an official outfit and attempt to re-equip it via the outfit drop-down, no change will be made to your equipment configuration:
This fact ensures that it is impossible to wear two outfits at once--one cannot equip four items using only three equipment slots. But it is possible to wear the Vile Vagrant Vestments and the Yendorian Finery due to the fact that the outfits have a hat, a 1 handed weapon, and an accessory and the other has an off-hand, pants, and an accessory.
Also, the "unequip all" button at the bottom puts you in your birthday suit, unequipping everything except for your familiar equipment (unless you have configured the Inventory Options in the Account Menu).
You can also specify custom outfits from any set of equipment you're currently wearing. Custom outfits have no in-game benefit other than convenience. If you already have 37 custom outfits and you try to create another, you get the following message:
If you click the Save as Custom Outfit button without having any text in the Outfit Name Box you get the following message:
Also also, if you try to equip a custom outfit containing a Mr. Store item while in Hardcore, you will be told "This outfit contains an item which is not equippable in hardcore. Nice try, though."