Move email between inboxes?

Move email between inboxes?

Is it possible to move emails from one team inbox to another? We would like to be able to have a single "catch-all" inbox for incoming requests, and then move the email to the appropriate department inbox. I was hoping we would be able to accomplish this through rules using comments or tags, but I can't find any functionality to move a message to a different inbox without replying to the message and CC'ing the other inbox email address.