For European licenses:
It used to be that Bombardier's Montreal TRTO had a JAA approved transition training from CL604 to CRJ.
Now they don't have it and based on rumour, it is not allowed anymore.
Vice versa conversion was not offered to my knowledge.
However, I know that some German operator with it's own TRTO has done some CRJ to 604 conversions, but I am not sure if that is possible either anymore.
For FAA, no idea.