For each standard class:

Barbarian: Great Old One Barbarian who leaves their damage to fate. Starting at 5th level they can choose to roll a d20 and add their wisdom mod (not proficiency) as their damage dice. (This actually averages below 2d12 damage.)

Bard: School of Mind who, starting at 7th level, can spend an action to channel the power of the heroes of old in a single attack. The next attack that may use a d20 as it's damage dice. You can do this a number of times equal to your proficiency modifier per long rest

Cleric: Force Domain. Starting at 5th level, When you make an attack on an enemy that is adjacent to another enemy and your attack is successful, you may choose to utilize a d20 for the damage dice. When you do, the adjacent enemies must make a dexterity saving through, taking the full damage on a fail, and half on success. The primary target must succeed on a Str saving throw or be knocked back 10 feet.

Druid: Circle of the Stars. Astral Weapon. Starting at 7th level, you call upon the power of the stars to enhance your attack. As a bonus action you may us this ability on a weapon you are wielding. On your next successful attack your attack die becomes 2d20. This ability lasts for 1 minute or until weapon is no longer in your control or you become unconscious.

Fighter: Brute. Furious Might. You channel your might and cunning into a single attack. Starting at 5th level you can forgo your extra attack and instead make a single attack. If you hit, use a d20 as your weapon dice.

Monk: Path of the Storm. Torrential Strike. You may spend 3 Ki points to upgrade your unarmed strike weapon die to a d20 for one turn or reaction.

Paladin: Oath of Chaos. Chaos Blade. On a Critical Hit you may choose to use d20 as your weapon die.

Ranger: Feysoul. Fey Strike. Your connection to the Feywild allows you to concentrate the powers of nature and magic to a single point. You may spend a bonus action to add a d20 of weapon damage to your attack. You may do this after the attack hits but before the result of the initial damage is known. You can do this one/long rest or twice/long rest starting at 12th level and 3/long rest starting at 17th Level.

Rogue: Black Hat. Calculated Strike. Your vast array of knowledge allows you to make the most of your opportunities in combat. Starting at 5th level, When you roll weapon damage for an attack and you are able to utilize Sneak Attack, you may choose to roll an Insight check. Use the result as weapon damage in place of your Sneak Attack damage.

Sorcerer: Fiendtouched. Fiendish Smite. When you make spell attack which deals Fire damage, you may spend 3 Sorcery Points as the fury of the 9 Hells reaches into the minds of your enemies. Each affected creature must make a Wisdom saving throw equal to your spell DC. Creatures take 1d20 psychic damage on a failed save and half as much on a successful one.

Warlock: Fate. Temporal Blast (Eldridge Invocation). Fate bends in your favor and allows you to concentrate misfortune to a single instance. You may choose to upgrade your Eldridge Blast to deal 1d20 damage for one turn. You may use this ability a number of times equal to your proficiency modifier before the next sunrise.

Wizard. School of Kinetics. Kinetic Surge. Once per long rest, you may upgrade the damage dice of any cantrip to d20.