This idea has been merged into another idea. To comment or vote on this idea, please visit LMS-I-1079 Repeating Overdue Emails.
We have control over the enrollment (notification), completion, nudge, and failure messages on the course level BUT we do not have control on the overdue message. Rather, the overdue message can only be changed for the entire system per language in message templates. This is a problem. I suggest you move the overdue message control to the course level.