I believe the fixed stock that fits the Steyr TMP will also fit the SPP. However I have not been able to locate any for sale. If you decide you want to add a Red Dot/Reflex sight the TP9 upper housing will fit the SPP and has built in picatinney rails. Check out www.dsarms.com
For what it's worth, we've had members post up reviews before of precisely the same NFA conversion - the general consensus from the users seems to be that it simply isn't worth it. If your heart is set on it, knock yourself out, but expect the novelty to wear off fast.
My Steyr M9A1 Evolution: v1.0, v2.0, v2.5, v3.0
Project MSAR STG-556:v1.0
Caracal Reviews: F and C
I had (operative word here is "had") the newer version of the SSP made by B & T. The piece as a pistol is okay and more of a novelty, but a well-built novelty. I thought to possibly add a folding stock (the B & T version had the mount for the stock on the back, IIRC) but decided that it wasn't worth it. After the novelty wore off I stopped seeing the point.
That said, I can fully undestand the the desirability of it, but luckily got out from under it for a minimal loss once I came to my senses.