@iobio
You have two options when it comes to Departments:
1.) You can Transfer a Ticket from one Department to another.
2.) You can Refer a Ticket to one or more other Departments.
With option 1 the Ticket's Department will be changed completely.
With option 2 it will give the Referred Departments referral access to the Ticket meaning they can view and post Internal Notes but they can not send a Reply to the User (and any CCs). The Ticket's main Department will still have full access to the Ticket and can remove the Referrals when needed.
Both of these options require the Agents to have the appropriate Role Permissions for the Ticket's Department.
Cheers.
