Jag-Stangs sound kind of wooly and undefined because of the lighter body wood (basswood) and lighter bridge mass + metal used (Jag-Stangs often have brass bridge saddles with = warmer tone)...too many of those elements and the output will be undefined. Also, the Jag-Stang comes with 250K pots stock, and those tend to cut down the volume and make the guitar sound thicker, that's why those pot values are used with single coil pickups usually.
I use mine for metal (that's the primary reason I bought it), but it has EMG pickups in it, and I added a no-load tone control, and a shortened wiring path to compensate for the light bridge, warm body wood, and brass saddles. EMGs in anything else would sound sort of tinny and flat, and it was still too wooly until I put a no-load tone control in there - a no load tone control is a tone control that cuts itself out of the circuit when turned all the way up so the guitar does not have the highs being drained off to ground by the tone pot while full up.
The kind of pickups one would want with a Jag-Stang would have Alnico 5 or Ceramic magnets, and would be tuned to have more high-end response to warm up the sound. For single coils, I could really see stock Mustang pickups doing an excellent job in the neck, I have an EMG SA in mine though, which sounds a lot like my 5.9K 66' Fender Mustang's neck pickup. That's one thing that draws me to the Jag-Stang, the pickup setup is balanced - fat pickup in the bridge, thin pickup in the neck, and it is very balanced out but still sounds very different.
Hopefully this spurs some ideas.
