This is more focused at tickets, but could be changed for anything that has a user selection (assign to).
In tickets, you have the option to select a user to look after ticket (assign user). Could you prioritse the notification to that user first, then to anyone who has the notifications for any ticket (When someone create a new public helpdesk case or helpdesk to groups you follow) . If the user is the assigned user, then they dont get the Follow notification.