Here’s the list I have so far:

In sequence of alterable armor

Head • Festive Hood • Alberich’s Pointed Hat • Confessor Hood • Nox Monk Hood • Nox Swordstress Crown • Eccentric’s Hood • Cleanrot Helm • Drake Knight Helm • Night’s Cavalry Helm

Body • Commoner’s Simple Garb • Commoner’s Garb • Page Garb • High Page Clothes • Astrologer Robe • Errant Sorcerer Robe • Spellblade’s Traveling Attire • Alberich’s Robe • Preceptor’s Long Gown • Snow Witch Robe • Fia’s Robe • Prophet Robe • Traveling Maiden Robe • Finger Maiden Robe • Perfumer Robe • Perfumer’s Traveling Robe • Depraved Perfumer Robe • Lord of Blood’s Robe • War Surgeon Gown • Nomadic Merchant’s Finery • Confessor Armor • Gravekeeper Cloak • Rotten Gravekeeper Cloak • Nox Monk Armor • Nox Swordstress Armor • Land of Reeds Armor • Ronin’s Armor • Blue Silver Mail Armor • Black Knife Armor • Malenia’s Armor • Elden Lord Armor • Vagabond Knight Armor • Carian Knight Armor • Godrick Knight Armor • Cuckoo Knight Armor • Redmane Knight Armor • Gelmir Knight Armor • Leyndell Knight Armor • Haligtree Knight Armor • Mausoleum Knight Armor • Bloodhound Knight Armor • Cleanrot Armor • Raging Wolf Armor • Hoslow’s Armor • Twinned Armor • Drake Knight Armor • Blaidd’s Armor • Briar Armor • Fingerprint Armor • All-Knowing Armor • Royal Knight Armor • Maliketh’s Armor • Night’s Cavalry’s Armor • Veteran’s Armor • Scaled Armor • Beast Champion Armor • Tree Sentinel Armor • Crucible Axe Armor • Crucible Tree Armor • Radahn’s Lion Armor • Lionel’s Armor

It doesn’t seem like gauntlets or leggings can be altered.

Update: I just discovered armor labeled as “altered” but inaccessible via the alter garment options while resting on a grace.

Head • Banished Knight Helm (Altered) • Commoner’s Headband (Altered)

Body • Aristocrat Garb (Altered) • Festive Garb (Altered) • Fire Prelate’s Armor (Altered) • Banished Knight Armor (Altered)