The Gloom Stalker Ranger looks like a pretty excellent 3-level dip for a Crit build, specifically for Dread Ambusher
"You can give yourself a bonus to initiative rolls equal to your wisdom modifier. At the start of your first turn of each combat, your walking speed increases by 10 feet. If you take the attack action on that turn, you can make one additional weapon attack as part of that action. If that attack hits, the target takes an extra 1d8 damage of the weapon's damage type"
With the Fighter's action surge, you can make two attack actions on your first turn and get two extra attacks from this, if you have Haste, you can take yet another attack action and get a third attack from this. you also get an extra d8 of damage, naturally doubled on crits.
If we really wanted to go deep on this, we could run something like:
Wood elf Fighter(2)/Paladin(12)/Rogue(3)/Ranger(4)
Rogue for Assassinate, Fighter for Action Surge, Ranger for Dread Ambusher (which also gives +Wis to initiative) and Paladin for Haste and Divine Smite.
We get 3 ASI, which would be +2 Dex, Elven Accuracy (+1 Dex) and Great Weapon Master for the free bonus action attack on a crit
On our nova turn, we can make 9 attacks: 3 from our Attack Action, 3 from Action Surge, 2 from Haste+Dread Ambush, and 1 bonus action from GWM. We get 3d8+sneak attack+divine smite extra damage.
We could also rework this to use Half-elf, drop some Paladin levels for 3 levels in Hexblade/Blade warlock, and get Cha to attack, but that makes you more MAD, especially since you're losing another ASI.
You have to get 13s in 4 stats to use all those classes, plus you miss out on a higher crit range. The extra attacks are nice though. Also the sneak attack and GWM won't work together.