Create a connection type in the microsoft apps to allow access without a user.
I don't know the particulars of what would be required on the Make side, since you'd need to pass the access token from module to module (or else have the backend auth library cache the token and be shared by modules).
This would allow the creation scenarios which can do things like send emails through multiple users, or attach files using their individual onedrive accounts.
Example use cases would be if an integration to an application where user generated events need send emails from user that generated the event - and the sent mail needs to be stored in the users mailbox for sending. Or storing and linking to files in the individuals onedrive.
By allowing a userless application such as this, its possible to create apps which serve many users with a single scenario.