Shared Mailbox integration

You can setup a shared MS account integration for one of the accounts as a second integration. Then, setup email syncs for those records where you want them to sync. There is a dropdown to select which integration to use before clicking the sync button. 

On the add-in side, if you wanted to add individual emails, you would need to sign into the shared account and access the add-in that way. You wouldn't need the second integration that way, your current integration should be able to query for any shared emails.