I'd dispute the comments that the tone comes from "processors, the signal chain, and perhaps overdriven tube overtones." Plug a PRS or a Les Paul or a Strat or a Flying V straight into an amp - are you going to get much tone without overdriving the tubes? I think we can even forget the processors and the signal chain, and I really don't think many guitars sound great without overdriving the tubes. What's the guy's point?
If someone knows where that file is on the net, which is an interview with Steve that appeared on a CD with UK's Guitarist magazine. Basically, Steve demo'd the (then new) BSB using a Laney LC-15 (£200 amp) an OD-1 and a Crybaby. That's a pretty low-tech chain.
One of the things he demonstrated was the tonal variety inherent in the Jems, and it's great fuel for your reply. He plays a few distinctly non-pyrotechnic pieces.
I'd rip the CD but it's back at my other house. I think it might even be the file here:
But I can't check it right now.
If we use the same setup I've described above, any guitar is going to bring its own colour but not masses of tonal variety (PRS does have a fair bit more variety than a Les Paul, granted). It's not strictly whether another guitar would be useful that's under debate; specifically, the first point the poster raises is whether or not the Jem has any tone of its own. Well, I'm very surprised that an owner of a Jem can dismiss the pickups so easily if nothing else. The comment about the neck is related, but slightly different.
Let us know the response you get.