My idea is to bring back the Mystic which was removed prior to the release of Diablo 3 with the main function of enchanting items - but done slightly differently by focusing on which class you'd like to add then enchantment for, and adding the chance of adding a negative stat.
Instead of using tomes, scrolls, levelling the Mystic etc I would suggest using gold only which would scale with the item level and rarity.
Say for example you pick up a superior hand crossbow, you could go to the Mystic and pay 1000 gold to add a random Demon Hunter affix - this could range from Dexterity, Critical Hit Damage, individual skill damage increases, group skill bonuses (all archery skills do x% more damage etc) and so on. Or you could pay for a generic affix - Vitality, damage increase, life on hit etc.
The mystic would generate a random name exclusive to enchanted items and a new colour would be shown for the hand crossbow's tooltip (orange, purple, whatever), however at this time there would be a chance that the "cursed" prefix appears on the item's name and the weapon's tooltip colour turns red - the Mystic's ritual was flawed and a negative affix has been added.
Negative stats could include things such as -ve % to movement speed, attack speed, life degeneration, chance to heal enemies on attack, lower item durability, chance skills use more resources etc.
Any item could be enchanted multiple times, with affixes scaling based on items level, however the cost, chance of a negative stat and impact of a negative would increase with each positive affix the item has i.e.
0-1 positive affix, 1% chance of a minor negative affix
2 positive affixes, 5% chance of a minor negative affix
3 positive affixes, 10% chance of a negative affix (of which 80% minor, 20% medium)
4 positive affixes, 20% chance of a negative affix (of which 50% minor, 50% medium)
5 positive affixes, 30% chance of a medium negative affix
6 positive affixes, 50% chance of a medium negative affix
7 positive affixes, 50% chance of a major negative affix
and so on
Obviously the above could be smoothed out a lot better than that and could perhaps take into account things like main stats etc, count how many times the same affix has been added etc.
I think the above would give players a chance to do something with all of the grey, white and even blue items which are left on the floor and add a bit of excitement on how far you push your luck in creating the perfect items whilst taking gold out of the ever increasing pool.