Can I enchant additional affixes or effects onto items?

No. You can only reroll existing affixes into new affixes of the same category* (vit->armor). I.e. you cannot roll a secondary affix into a primary affix.

There are some limitations for this rerolling:

• You cannot add a second affix that's existing on the item. So no doubling up of Int affixes, for example.
• You cannot add a resist all or (specific resist) affix onto an item if the other exists already. This is to prevent doubling up of resists (OWE nerf for monks basically)
• You can only add affixes that can be found naturally on the equipment slot. Weapons will never roll +armor, for instance, and bracers will never have a socket.
• You cannot reroll specific legendary mods (The only one I know of so far is the increased fire damage taken on Andariel's helm). You also can't reroll the orange stats, but that should be obvious.