Is it possible to add extra AC onto "Adamantine Armor" that we find as treasure? As the Adamantine is uncommon, I would assume that the highest magical increase could be +2, making it Legendary.
I haven't found much about how to craft magical items in 5e (I do understand why that is) or whether it's possible to alter enchantments on existing items, so I thought I'd ask.
If you're playing an Adventurer's League game, the answer is a hard "no" unless you were given a certificate authenticating your character as possessing that item.
If you're playing by strict RAW, using only printed magic items, the answer is also "no", because the Adamantine Armor and +2 Armor are two separate magic items. While the DMG and Xanathar's Guide to Everything have rules for the process of creating new magic items, neither have any rules for the process of improving the power of existing items.
The DMG states in the Chapter 9 Section on Creating Magic Items:
The magic items in chapter 7, "Treasure," section are but a few of the magic treasures that characters can discover during their adventures. If your players are seasoned veterans and you want to surprise them, you can either modify an existing item or come up with something new.
While the existing list found in Chapter 7 of the DMG is not exhaustive, it is an actual list of items that are immediately available. As with nearly everything in D&D 5e, the DM can modify or create pretty much anything - but that doesn't make those modifications/creations any less 'homebrew.'
This is very similar to the language in the PHB regarding Equipment (Chapter 5):
table collects the most commonly available types
The types listed for Armor, Weapons, Magic Items, etc. are actual lists and not just examples - they are just not exhaustive lists.
If you are looking for an existing set of Adamantium Armor +2, you aren't going to find it in the books. It 100% requires the DM to create it and determine it's rarity and cost. They can refer to the guidelines for support in doing that, but the item isn't an existing item.
There are no existing guidelines in any rules book about upgrading a magic item. If and how this would be done would be a homebrew by your DM.
Now that season 8 of AL has come out and explicitly said that +1 Mithral “was a mistake and never existed” I’d argue that applies to this too.
From what I've seen (particularly under "Modifying an Item" on p. 284 of the DMG), it's not only possible but would be plausible.
If you think about it, adamantine armor (and, by extension, mithral armor) are simply the metal that the armour is made from, similar to iron or steel, but they have special properties which give them their respective abilities.
It may be harder to craft an enchantment onto the armour, and it may be limited as to what enchantments can be placed on them, but personally I would rule that it can be done.
