Notification of assignment submissions

At our college we have have a course page for each cohort and a number of tutors use each cohort page.  At the moment if a tutor sets an assignmentall the teachers enrolled on the course page get  email notifications for each assignment set when the student submits work, which is not ideal. Is it possible to choose which tutors gets submissions for each assignment? I am aware you can turn the notifications off, but I would like to get notifications of submissions.

Thanks

Mary