Hi @Brian_Postow 
That’s a great question, and I’m happy to help on this.
It is not possible to move tasks between workspaces, and we typically recommend teams and departments from the same company to use Teams in Organizations rather than separate Workspaces. You can move tasks between projects in different teams within the same Organization, and you can also add tasks to multiple projects within the same organization. You can see more information about the difference between Workspaces and Organizations here.
Additionally, there are lots of different ideas from community members on a similar thread about moving projects between workspaces here: Moving Projects Between Workspaces/Organizations and the third-party app Kothar will allow you to copy projects and tasks from one Asana workspace to another.