The Thri-Kreen in the Monsters Manual (page 288) have four arms. The benefit they seem to gain from this is the ability to use a two-handed weapon while wielding another weapon.
Without houseruling anything, a creature with extra hands would just get more hands wherever the rules call for hands. For example, a weapon with the Two-Handed property "requires two hands to use", so you could potentially wield two of those (although, depending on the configuration of the arms, this may not make any physical sense). Grappling and some spellcasting require a character to have a "free hand". A four-handed character would have a free hand even while wielding a two-handed weapon, or even two light weapons and a shield. In fact, it's perfectly within RAW for a Thri-Kreen to grapple an enemy using its free hands while wielding a two-handed polearm.
An obvious question is whether the character would be able to wield four weapons and make four attacks. RAW says no. The rule on Two-Weapon Fighting would still apply as written, and both weapons need to have the Light property, unless you have the Dual Wielder feat.
This rule from the Dual Wielder feat becomes interesting:
You gain a +1 bonus to AC while you are wielding a separate melee
weapon in each hand.
Does that mean you need to wield melee weapons in all of your hands to gain the benefit? As written, it's not clear, but from context (it's dual wielding after all), you'd just need to have weapons in at least two of your hands. The intent is likely that you gain the benefit because you cannot use a shield, so perhaps the rule should be that you have a weapon in two hands and no shield.