Many of these are "likely enough to be sustainable, maybe", so this is just for fun.
High Elf Bard (Swords) 12 / Wizard (Bladesinger) 2 / Monk (Kensei) 5 / Cleric (Forge) 1
Assumes 2 encounters of about 3-4 rounds between rests.
+2 DEX, +1 INT from race plus 4 ASIs = 20 INT, 20 DEX using Standard Array
Studded Leather: AC 12 +5 DEX
Bladesong (2/short rest for 1 min): +5 AC
Defensive Flourish (5/short rest): +d10 to AC with attack - +5.5
Forge Cleric: +1 Armor
Monk Patient Defense (5/short rest): Dodge as bonus action
Monk Kensei Agile Parry: +2 AC
Shield of Faith: +2 AC
Mostly Sustainable AC: 32.5 with disadvantage. (Disadv only 2+ round)
Shield: +5 when needed, which brings things up to "20 only hits" area.
Notes:
While many monk abilities turn off with armor, the Ki powers like Patient Defense do not. However, this does mean that the Unarmed attack made to enable the Kensei Agile Parry is STR based and doesn't get the martial arts die for damage if it hits.
So this requires an Attack action, one attack (likely with a rapier that is a kensei weapon) and one unarmed (STR based). Lucky we have Extra Attack from the monk. One must hit to trigger the Defensive Flourish, which also adds to it's damage. Then bonus action to spend a ki and Dodge. The Shield of Faith needs to have been already up. The first round will be without Dodge because the bonus action is used initiating the bladesong.
Defensive Flourish doesn't quite last long enough. Bard 14 would give a d6 whenever not spending a bardic inspiration, but that kills ASIs and other things. But we do have plenty of spell slots for Shield to help carry over.
If this was really good ability score rolls, we could go 20 WIS as well, drop the armor (and the forge cleric level) and gain an extra +2 AC with Monk's Unarmored Defense. (12+1 forge+5 dex vs. 10 + 5 wis + 5 dex), and that would also enable all the monk unarmored abilities.
Oh, and this does assume pre-casting Shield of Faith. Since others assumed consuming potions and the like I assumed that was on the table. Magical secrets could have gotten us other +2 AC concentration spells as well.
EDIT: And I'm a dumb-donkey. I was originally playing around with Bard 14 for the constant d6s, so I was only thinking about having enough of a CHR to MC into bard. But up there I'm assuming 20 CHR for 5 defensive flourishes per short rest.
EDIT the SECOND: I'm not just a dumb-donkey, I'm also an unobservant one. Mage Armor increases the AC by 1 and enable the Monk Martial Arts. (No, not Monk Unarmored Defense. Not using that.)
A lot of new tools I was not aware of here. Awesome.
I want to play with this...
HighElf +2 dex +1 int allows of Bladesinging, ok.
I don't think you can get three 20 stats with Standard array and 4 ASI increases.
I will drop Forge Cleric. Blessing of the forge requires armor.
Str and Con are drop stats, wisdom is not used for AC, so 13.
Standard Array: Str 8, Dex 14, Con 10, Int 15, Wiz 13, Cha 12
ASI
Wizard lvl4: +2 Dex(18) | Wizard lvl8: +2 Dex(20)
Monk lvl4: +2 Cha(14)
Bard lvl4: +2 Int(18) | Bard lvl 8: +2 Int(20)
Adjusted Stats: Str 8, Dex 20, Con 12, Int 20, Wiz 13, Cha 14
Wizard tadition of Bladesinging lvl 8:
MageArmor 13+5 Dex = AC18
Bladesong (2/short rest for 1 min, Intelgence modifier): +5 AC
Haste (+2AC)
Shield Spell (+5AC)
Subtotal (Static: AC18 Sustanable: AC23 Temperary/Consentraion spells: AC30)
Monk Way of the Kensi lvl 4 (characer level 12):
Agile Perry +2AC
Dodge action or Patient Defenst bonus action
effective +5AC
Subtotal (Static: AC18 Sustanable: AC25 Temperary/Consentraion spells: AC37)
Bard Collage of Swords lvl 8 (characer level 20):
Defensive Flourish (Charisma modifier=2/short rest): +d8 (lvl 5) to AC with attack. +1 to 8AC
Total Static: AC18 Sustanable: AC23 Temperary/Consentraion spells: AC31-38
