Technically yes, Users can only have one department set. However Departments access are controlled by groups. Users can also have a group set. So you can be a member of group FOO that has access to Department Alpha and Beta. And also be a member of Department Delta. Since Department access is controlled by groups, multiple groups can access a single department .
Admin panel -> Staff -> Click on Staff Member.
set Assigned Group (drop down)
Set Primary Department (drop down)
You can also set Assigned Teams.
Go to Admin panel -> Staff -> Departments -> Click on the department.
Set Group Membership: Extend membership to groups with access. (Alerts and notices will include groups)
Set Department Access: Check all groups allowed to access this department.
Note that most of this functionality was introduced in 1.7.