Azure Enterprise Application accessing a single mailbox

Hey Tony, 

You may want to explore how Azure Administrative Units can help in this situation. 

Using AU's you can delegate typically admin accounts to access 1 or many users/mailboxes. 

However I am unsure if AU's can handle Shared Mailboxes since the usecase for AU's is to delegate admin access to scopes of users for administrative tasks. Furthermore you need delegate access to an application object rather than a privleged user object. So this is something you may want to explore. 

Check out:

http://www.deployazure.com/security/identity/azure-ad/azure-ad-administrative-units-in-exchange-online/

and

https://docs.microsoft.com/en-us/powershell/azure/active-directory/working-with-administrative-units?view=azureadps-2.0

Hope this helps!