I'm not an expert by any means, but by crossing 2 or more chicken breeds you would get mutt chickens with probably different copies of genes. This is a reason for hybrid vigor. However, by continually crossing the continuing generations of offspring, the genes would tend to stabilize where it would be possible to end up with completely new breeds. What characteristics the new breeds would have is unknown.
For example, using the offspring of hybrid Red Stars and continuing to cross the ensuing generations, you would eventually end up with new stable breeds involving alot of recordkeeping.