The order is the same as for the displayment of the enchantments in the item's description. The device will improve the first enchantment on the item. Not only could it get items closer to the desired level, it can do more - it can increase the level beyound maximum, allowing enchantments like Fortune IV, or Sharpness VI. You have managed to create an Overchanting table, which is able to increase the level of enchantments on the item by one.
You have managed to push that limit a little bit further. However, there always seems to be a limit to the magic infused into the item. Thaumaturges have also discovered a way to do the same with an Infusion Altar, using it to make items stronger. 'Thaumaturges often use their magic to infuse regular mundane items with magical force, making them better.
