Building a JEM or UV from scrap parts.
I love project guitars, to me they are better than new ones, especially when I have the time/money/energy to do it!
Budget and patience is a key player.
I recommend finding a used RG550/570 ($275-350). *It is the closest you'll get to the Jem. *
Assuming that you're not handy with routing, send the body to Chris Tatalias at East Coast Music Mall, for uder $100 he'll give ya an exactly proportioned monkey grip. *(now you're in for about $450) *
If you watch eBay, you may even find a cool neck, like maybe a PGM neck (cool reverse headstock!) or maybe even a USA Custom with offset dots (or shark teeth if ya like that kind of thing) or the queen mother, a Jem neck! *Now you're at about $600+ depending on which neck you use.
The you can finish (or unfinish if you like!) and swap your electronics out if you so desire. *
If you're going to get more involved, you may as well buy a used Jem and refinish or mod the electronics.