I'm not talking about copying (i.e. importing/exporting, which requires replacing all of the website's tracking codes) but about cases when a container was opened in the wrong account and/or when a merge is required.
Is it possible?
After wishing I could do the same and researching it, I have found the answer to be: No.
You can import and export, but you cannot modify the common GTM ID (ie. GTM-XXXXXX), and since you must import into an existing container, whatever you import is associated with that container ID.
It would be very nice to be able to move these around, but I'm sure the reason for not allowing it is that Accounts might be owned and managed by different companies or users, and moving containers between such environments could become very complicated just in terms of permission.