After talking with the Support Forum Team and Cory the current BEM 1.3 standard would support this request, albeit a little clunky. The BEM 1.3 Wrapper API only contains a POST operation so the sender would have to send the transmission to you. Or it could be sent via SFTP.
Note that this functionality is being addressed in a future specification which is currently in committee testing. This functionality will include a "get" function for the receiver to initiate this process rather than the sender.