Somewhat inspired by this question: Can I use multiple hands for one attack, using this 6-Handed-Ones homebrew race?
As I started to explore with my question about playable Kuo-Toa, I'm interested in seeing what other humanoid monstrous races could be converted into playable races as per the monstrous races from Volo's Guide to Monsters? They've already got Orcs, Kobolds, Goblins, Hobgoblins, Bugbears and Yuan-Ti Purebloods, and now I've added Kuo-Toa (to my own personal library of playable races, I mean), but others that caught my eye included the Thri-kreen, an ant-like humanoid race with four arms (MM, p. 288).
At the time I steered away from them because of the multiple pairs of arms thing, but this "6-Handed-Ones homebrew race" question has inspired me to ask anyway; if I were to make, for example, a Thri-kreen playable race, what should I take into consideration with regards to the fact that they have four arms/hands?
What springs to mind is the fact that such a PC could potentially hold a shield, a greatsword and a spellcasting focus all at the same time, which seems quite powerful. Would a PC having multiple arms be inherently unbalanced due to such situations as this, or is there a way for such a racial trait to remain balanced in comparison to the existing playable races?
NB: There may be other concerns with converting Thri-kreen over to a playable race, such as the fact that they have strong natural armour providing a high base AC, poisonous bites, and the fluff text says they don't need sleep; I haven't begun to think about any of this yet because I stopped at this first hurdle – multiple pairs of arms. Hence I'd like answers to keep away from these other concerns and only focus on this one issue regarding multiple pairs of arms.
Best Answer
Simply allowing more arms is overpowered
Allowing a PC to use a two-handed weapon with a shield is overpowered indeed. The game wasn't created with that in mind: either your character use a two-handed weapon to deal more damage or use a shield with a one-handed weapon, trading-off the higher damage for better protection.
By simply allowing a PC to have four-arms, without limiting what it can do with those will surely break the game. The PC will be able to ignore a lot of "exclusive options", trade-offs it can simply avoid; the two-handed weapon with a shield is just one of them.
Spellcasting with a sword and shield (without War Caster), wielding a shield with a spellcasting focus and dual-wielding, using a hand crossbow with an shield, and any other situations that can't happen when you only have two arms are some of the trade-offs a four-armed creature can avoid.
So, how to balance it?
If I were to create a Thri-Kreen race, I would limit what it can do with those extra arms. A good starting point is to limit what interactions can be done with those extra arms. The Trunk feature from the Loxodon (Guildmaster's Guide to Ravnica, page 18) gives us a good starting point:
Of course, the thri-kreen extra arms aren't like a trunk, so it needs tweaking. I would reduce the number of pounds it can lift, and well, a thri-kreen can't use arms as a snorkel. I would also remove its ability to grapple or interact with a creature; their extra hands are small. Instead, I would allow them to have "one additional interaction with an object or environment, for free, during your turns".
The most important limitations of extra arms are in the second paragraph. I would never touch those, because that's where the majority of problems lies with extra hands.
As Matthieu M. pointed out in the comments, a good explanation for why shouldn't a Thri-kreen extra arms be limited, is that the creature's brain is limited, and can't coordinate so many tasks with the required precision.