I would like to suggest the following options to be built:

 

1) Option to disable auto response to an email addresses within the same domain.

 

For example support@domain.com has auto-responder (where the auto-esponse is more for customers). So with this option if admin@domain.com sends an email to support@domain.com, admin@ will not receive the auto-responder.

 

2) Similar to 1, create a bypass list. So users can enter an email address where they know a auto-response does not need to be sent back.