Well, I don't know exactly how much gain the Starcaster has, but you can try using a distortion pedal in combination with the amp gain.

The best way would be to take your guitar to a music store and try a couple of amps and see if there is a difference in how your squeals sound.

With humbucker pickups (like on a Les Paul) the squeals will also be louder than on a guitar with single coil pickups (like a standard Fender Strat).

Vibrato helps a lot with the squeal effect though.