I know you can configure notifications for "All new conversations & messages initiated with the account" and you can configure "Notify for new messages on a conversation I am assigned to" but it would also be helpful to be notified for new messages and conversations on "Unassigned" contacts.

The use case being you uncheck the All setting so you don't get everyone else's assigned contacts and you check the box for assigned ones but that leaves the unassigned to fall through the cracks.