Not trying to sound like a jerk here, but I don't think you'll be getting too many replies on this for two reasons:
1) if you "want more than that" then, fundamentally, you want something other than Vai's tone.
2) Steve plays a particular rig for a particular sound. Sure, much of one's tone is in their technique, but if he's using an alder body superstrat JEM w. EVOs through an EL34 amp, and someone wants to get his sound through, say, a mahogany guitar w. a shorter scale, different pickups and an EL84 based amp, I really can't see why they're even trying.
You're first going to have to define what "more than that" means, and then folk here may be in a better position to help you.