Can a user be in more than one department?

Yes. Open the person's profile, go to the Production Roles tab, and click Manage Groups beside the production. On the Departments tab, check every department they belong to, then save. The same screen has Groups and Roles tabs, so someone who's both a designer and a stage manager can carry both.

You'll need permission to manage groups on that production. Departments mostly decide who sees shared files, so someone in two departments sees files shared with either one.