This is something we have on our roadmap. Not necessary implemented as statuses, but more like a checklist attached to a note.
As you say, supervisors want to add things that the artist should do to make the note complete. So instead of having a status that you change, the supervisor can add a checklist when creating the note and any recipient of the note have the ability to check things of the list. When all items have been checked, the note is shown as completed.
Of course, notes with unfinished checklist items should be queryable from notes and in the inbox.
Exactly how this will work is not fully decided yet and any feedback on the matter is appreciated.