I know this question is over 5 years old and that it specifically asks for AC without allies' buffs, but I know I was curious enough to look for it with allies' buffs, so I'm sure someone else is as well.
I found a way for an AC of 88 with the support of 4 allies and without using any ability score raising items or stacking any bonus from the same source. This build was created just after the release of Tasha's Cauldron of Everything.
Character Build (receiver of AC)
Race: Warforged. This is to receive a +1 bonus while wearing armor thanks to the Integrated Protection racial trait.
Class 1: Alchemist Artificer (10 Levels). With 10 levels in Artificer, you gain access to the Magic Item Adept feature which allows you to have 4 items attuned at once. Additionally, the Alchemist subclass gives the Expiremental Elixir feature which, when an Elixir of Resilience is created and consumed, gives you +1 AC.
Class 2: Forge Domain Cleric (6 Levels). With 6 levels in the Forge Domain, you have the Soul of the Forge feature which gives you +1 AC when wearing heavy armor. Use the ASI at 4th level to take the Fighting Initiative feat and select Defense to earn another +1 AC when wearing armor. This will also give us access to the spell Shield of Faith buffing our AC by +2.
Class 3: Wild Magic Sorcerer (2 Levels). This one is a bit of a stretch, but we are looking for the highest AC possible in DnD not the highest realistic AC. With 2 levels in the Wild Magic subclass, you gain access to the Wild Magic Surge feature which allows the DM to ask for a 1d20 roll after you cast a spell, and on a natural 1, you roll on the Surge Table. If you roll a 51 or 52 on the Surge Table, you gain +2 AC.
If you've been keeping track, with just Race and Class, we are currently at an AC bonus of +8 so long as we include heavy armor below.
Plate, +3. This gives us a bases AC of 21.
Shield, +3. This gives us a total additional AC of +5.
Defender Sword. Attunement Slot 1. While wielding this weapon, we can have another +3 AC if we convert it's magic bonus to AC on our previous turn. (Be sure to use a one-handed sword for this to be able to wield our shield.)
Cloak of Protection. Attunement Slot 2. This gives us +1 AC.
Ring of Protection. Attunement Slot 3. This gives us +1 AC.
Ioun Stone of Protection. Attunement Slot 4. This uses our additional attunement slot earned earlier and gives us +1 AC.
So Far, we have a total AC of 40.
Valor Bard (15 Levels): This ally will give you a die of Bardic Inspiration which, thanks to Combat Inspiration, allows you to add 1d12 to your AC as a reaction. Like with Wild Surge earlier, we will assume the best roll possible which in this case, adds +12 to your AC.
Cavalier Fighter (7 Levels) and Cleric (3 Levels): With 7 levels in Cavalier, this ally can buff your AC by 1d8 with it's Warding Maneuver feature. Again, we'll use the highest roll possible meaning +8 AC. Additionally 3 levels in Cleric gives access to the spell Warding Bond which will increase your AC by another +1.
Oath of Glory Paladin (15 Levels): A Glory Paladin gets the feature Glorious Defense which can raise your AC by it's CHA Modifier which we will assume to be +5. This Paladin is also capable of casting Haste for another +2 AC.
Battle Master Fighter (18 Levels): Using the Bait and Switch combat maneuver, this ally can raise your AC by 1d12, so for our sake, +12 AC.
Thanks to our allies, we now have an AC of 80.
Cover: With 3/4 cover, we gain another 5 AC bringing us to 85.
Marriage: If either you, the Paladin, or the Fighter/Cleric cast the spell Ceremony and held a wedding within the last 7 days between you and another ally listed above, you gain +2 AC. This brings us to an AC of 87.
Rod of Alertness: If one of your allies has attuned to and placed this magic item, you gain your final AC bonus of +1 for a grand total of 88 AC.
With a specific AC build for yourself, specific support builds for 4 allies, 7 magical items, 4 spells, a wedding, and 3/4 cover, there is a 1 in 3,456,000 chance that one can achieve an AC of 88 without stacking sources.