High impact polystyrene, as you probably know, is polystyrene with about 8-10% butadiene rubber particles in it to give the added impact resistance. That means the continuous phase is polystyrene and so you need a solvent for PS. Solvents that I am nearly positive will work include toluene, acetone, THF and MEK. There are others too if you need more alternatives. Such solvent welding should work although the welded joint is likely to have somewhat lower strength than the rest of the part.