Using shared mailboxes (auxiliary and tactical). Requesting a means to sync with CMS (eg IMAP) rather than download and delete from CMS (eg POP3).
I think I understand the use case you're trying to solve for but I believe the mental model of a shared mailbox is incorrect. When using auxiliary or tactical, users are simply sharing credentials with each other. As far as I know there is nothing on the Winlink protocol that allows for a IMAP type behavior. Once a message is confirmed downloaded by a client, it's no longer available for download.