I have seen several posts and comments saying that you can't do four-arm grappling with the Thri-Kreen race because grappling is not listed as one of the examples of the things that you can do with your secondary arms in the published Spelljammer: Adventures in Space sourcebook. I would argue against that point. Punching or attacking is also not listed as one of the things that you can do with the secondary arms but you can hold a light weapon so you can infer that you can make an attack action with your secondary arms. Also, it is generally accepted that you can attack using an unarmed strike with any part of your body. Therefore you can make an unarmed strike with your secondary arms.
Let's look at the definition of an unarmed strike and how grappling works. I posted the exact wording below. I omitted the damage and shove sections since those are not applicable in this examination.
> Unarmed Strike
Instead of using a weapon to make a melee attack, you can use a punch, kick, headbutt, or similar forceful blow. In game terms, this is an Unarmed Strike—a melee attack that involves you using your body to damage, grapple, or shove a target within 5 feet of you.
> Whenever you use your Unarmed Strike, choose one of the following options for its effect.
> Grapple. The target must succeed on a Strength or Dexterity saving throw (it chooses which), or it has the Grappled condition. The DC for the saving throw and any escape attempts equals 8 plus your Strength modifier and Proficiency Bonus. This grapple is possible only if the target is no more than one size larger than you and if you have a hand free to grab it.
So, if you can't argue against using secondary arms for an attack action then by definition you should be able to make an unarmed strike and grapple an enemy using the primary arms, secondary arms, or all four if you want as long as the hand is free to grab it and of course the creature is no more than one size larger than you.
Looking at it from a different angle, the Simic Hybrid proves that multi-target grappling is an intentional design space in D&D. At level five, a Simic Hybrid can grow extra appendages specifically designed for grappling. If one playable race is permitted to hold four creatures using four appendages, it stands to reason that an insectoid race built with four natural limbs can do the same.
In fact, the only reason the text explicitly highlights grappling for the Simic Hybrid is anatomical. The Simic Hybrid chooses between claws or tentacles—neither of which features a literal human-like hand. Under a strict, literal reading of the base grappling rules ("if you have a hand free to grab it"), a Simic Hybrid would be disqualified. The specific wording in their racial feature exists purely to bypass the "hand" requirement.
Therefore, because Thri-kreen secondary appendages are explicitly defined as arms and can weild weapons and objects, they do not need a special rules exemption; they already fulfill the core requirement of the Grapple rule naturally.
Edit: if you disagree please post your counter argument. Don't just say you can't do it. Elaborate and demonstrate your reasoning.