I've read that if you manifest soul blades in each hand that you can only make 2 attacks with them at most since they each disappear after your attacks.  But what if you have your Astral Arms deployed?  Can you now produce up to 4 Soul Blades and make 3 attacks with them?

No, Astral Arms cannot wield weapons; they can only make unarmed attacks.

Not only what Zeekec said about them not being able to wield weapons. But the reality is that Astral Arms don't even have to have hands. They could just as easily be anvils, Bear or Tiger Paws or something else.

Yeah, just a fun thought since the arms can take any form that you want them to and they can be used to make unarmed strikes.  There's also the thought that the soul blades aren't material either so it makes an odd dynamic.

I think that a generous DM might allow the combination of Soul Blades and Astral Arms, since there's a logical argument for both to be basically concentrated energy rather than pure physical objects, but going purely off of RAW it's not possible.

Quote from TransmorpherDDS >>

I think that a generous DM might allow the combination of Soul Blades and Astral Arms, since there's a logical argument for both to be basically concentrated energy rather than pure physical objects, but going purely off of RAW it's not possible.

 That makes sense, my DM gave me a homebrewed "astral sword" that did 1d8+DEX, could only be wielded by the Astral Arms, and took an action to summon. It ended up being very balanced, as well as fun.

Although not RAW I think it would be fine, for RP, if your arms were your blades. With a caveat that they act just as if you were wielding them in your own hands. You still would use DEX or STR, would not have reach, same number of blades, everything would be as if you didn’t have the arms and just attacking as a rogue, but in essence your arms and blades are intertwined. 

So no mechanical value but just flavor.