How to create a Business Address to manage and measure Incoming and Outgoing Messages.

I have a team using a Distribution Id which forwards the incoming emails to their personal Ids and the reply to the Incoming is sent from their personal Ids. This process of handling incoming queries is difficult to manage and measure productivity, timeliness. I need to create a Business Address where Incoming mail queue can be easily managed in terms of assigning, monitoring and reduce duplication of work. This BA address can use as a measurement tool to record productivity,Quality and timeliness