Can you mount both a turbo and a supercharger?

Yes, There's even some with a supercharger and twin turbos.

A "supercharger" is anything the increases the airflow into an engine above atmospheric, there for a turbo and a blower are both types of "superchargers". There are many applications of both turbo's and Blowers on the same engine and any combination of multiple of both, I.e. @ turbo chargers and 2 blowers or a blower and quad turbo's etc etc.