Breeding Japanese carp from different color variations

I used to help my father breed koi years ago. We usually bred kohaku and the other gosanke. I always wondered (and I would love to pose this question to experienced breeders) what if we were to combine carp from different varieties? For example if we had kohaku bred with tancho and shushui or ogon or asagi in the same spawning pond? What would the outcome be like and would individuals of a different color from their parents result? For example a spawning between a kohaku and a shusui suddenly yielded karasugoi ? Or is this genetically impossible?