Apart from coturnix japonica and coturnix coturnix, which are probably already crossed in the 'coturnix' quail we know, I wouldn't attempt any hybridisation. There are probably other species they can hybridize with - according to wikipedia there are 6 species in the coturnix genus, and my guess would be they can breed with all, though the offspring of some might be infertile.
But the other species are so rarely seen in captivity, they'd be much more valuable if kept pure. Also it'll be less risky for the animals - a 'rain quail' might not be able to live a stress free life with a coturnix quail, and hybrid offspring might not be as healthy as the pure species.