I know there are mods for robes over armor. Unless there is something in the base code of the game that prevents you from equiping more than a certain number of items it should be possible. I imagine it would just render whatever the top layer is. I'm not concerned about the looks, I just want the enchantment stacking.
I know in Morrowind You could have 2 rings and robes went over any armor, some armor didn't allow clothes underneath. Depending on what you had you could have up to 13 pieces of clothing equipped including rings and necklace. Shirt, pants, helmet, chest plate, right shoulder, left shoulder, right hand, left hand, leg armor, boots, ring, ring, necklace. It really made the time and effort of enchanting worth it. With Skyrim I feel like I'm better off just skipping it and using what I find, because without fail almost everytime I make a high end item I will find something better. Also by the time you get your enchanting that high in the first place you've most likely leveled up enough that you could run around naked and punch everyone to death.