The Travelers of the Multiverse Unearthed Arcana includes a playable insectoid race called the thri-kreen that has 4 arms, each of which is capable of wielding weapons, albeit with some limitations:
Secondary Arms. You have two slightly smaller secondary arms below your primary pair of arms. The secondary arms function like your primary arms, with the following exceptions:
- You can use a secondary arm to wield a weapon that has the light property, but you can’t use a secondary arm to wield other kinds of weapons.
- You can’t wield a shield with a secondary arm.
For example, a thri-kreen could wield a greatsword with their 2 primary arms and a shortsword with each secondary arm and then make one attack with each sword using Extra Attack and Two-Weapon Fighting, something that would be impossible for a 2-armed character. Still, this specific combo appears to be well-balanced, because the average damage is the same as simply attacking twice with the greatsword: 4d6+2*STR total damage if all attacks hit (and attacking with only the greatsword doesn't even require a bonus action).
However, one could imagine that this might not be true of all weapon combinations.
Is there any combination of weapons that will allow a thri-kreen, with their 4 arms, to deal more average damage than a 2-handed character with the same stats (i.e. same ability scores, same non-racial features, same class levels, etc.)? Or does the action economy prevent things from getting too, er, out of hand?
To narrow the scope of the question, you may assume that the only relevant non-racial feature is Extra Attack, but feel free to go into more detail if your combo depends on a specific class feature or feat.
(Obviously having 4 arms with hands has other benefits, such as being able to manipulate other objects even while holding 2 weapons, or wielding 3 weapons and a shield at once, but for the purposes of this question I'm only asking about damage.)
Reminder: Two Weapon Fighting only triggers from making an attack with a one-handed weapon, even if you take the Dual Wielder feat. So 2 Greatsword attacks + 1 Shortsword attack isn't possible with standard Extra Attack + Bonus Action.
(TWF): When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. [...]
(Dual Wielder): You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren't light.