Can you add another enchantment to an already enchanted item?

AFAIK, no. You can of course enchant an item with two effects once you reach Ench 100 (well, three effects if you DE the item from Ironbind that has both Soul Trap and Fire DMG....), but you have to have a "bare" item to do so.

On some items you can. Wuuthrad for example.

Isn't one of the Enchanting skill perks that you can put 2 enchants on one item?

Yes.... at 100 Ench.... but you still have to (normally) use an item "bare" of any enchants to begin with. Wuuthrad.... I don't know about. It's an ugly 2-hand axe. I don't ever use it.

Well this may very well change my plans. I was hoping to create some randomly enchanted deadric axes in the Atronach Forge. Then use the extra effect perk on them.