I don't believe this is possible. It's certainly not possible between the saveinit and shooting phase of the PSS. I did try using either a dummy alter statement between the two pss runs that you'd tried, but the save statements are effectively global and not ordered.
I also tried putting the save statement in an altergroup, but that's not supported.
So I think this is a good idea though - so please contact customer support and request an enhancement to provide a way to do this. Probably we need something like a "queued" save statement (similar to the "set" statement which is a queued options statement), where the save statement would be run in order like the analyses are.
In reply to Andrew Beckett:
I have also tried the alter/altergroup statements in the first place to vain. As you suggested let me suggest an enhancement through the customer support.