Or 1956 with UA
Before we get into this a word of warning: you could use the books and the Morgan Freeman method detailed in Acumen's highest ability score video for infinite damage, so that's the max, but following is the maximum finite I've found.
First of, make your character a lv. 17 Rogue Assassin, lv. 2 Paladin, and lv. 1 Mystic. You'll need 5 other members in your party: a druid, bard, 2 paladins, and a wizards. You're able to replace the wizard with a sorcerer, and one of the paladins with a cleric. Second, choose bugbear as your race. Choose Dueling as your fighting style for Paladin. Be a good alignment. Get the Martial Adept ability, along with any skill that lets you add your superiority die to damage.
As far as magic items go, we only need 1. Get a Vorpal Scimitar. Also obtain Purple Worm Poison.
Now is when things start getting desperate. We need 1 level in Mystic for the Brute Strength discipline. If you don't like UA, then sadly we lose quite a bit of damage, but you get a free level. Second, we must be in the plane of Mount Celestia. Good-Aligned creatures here benefit from the effects of the Bless spell, and along with that you need to somehow get a fiend there. We also must acquire the Boon of Luck, and 10 boons to increase DEX and CHA to 30, making this section easily the most controversial of all.
Time to put it all together. Have the druid in your party cast Flesh Rot Contagion on the fiend. The Bard needs to use bardic inspiration on you, and cast Bestow Curse on the fiend. One of the paladins needs to use Crusader's Mantle, while the other uses Holy Weapon on your weapon. The druid should then cast Elemental Bane on the fiend, choosing thunder. Finally, cast Thunderous Smite, Apply Purple Worm Poison, and sneak attack. On the damage roll for this attack use Boon of Luck, Bardic Inspiration, Divine Smite, 2 Uses of Brute Strike, Your Martial Adept ability, Channel Divinity Sacred Weapon, roll a nat 20, make sure your opponent is immune to Vorpal Insta-Kill, and Death Strike.
All damage dice gets doubled on a crit (I believe, I may be wrong about this), meaning you'll be dealing 2d12+2d10+12d8+50d6+6d4+25 damage, multiplied by 4 for Death Strike and Vulnerability you have 8d12+8d10+48d8+200d6+24d4+100 damage, and assuming you roll max on all of them:
1956 Damage. Nearly 2000.
Excluding UA like OP said it's 1860 damage.