If the user rates the staff member's support as a 10/10, allow the user to optionally provide written comments.
If the user rates the staff member under 10, require the user to include written comments to explain what the staff member could have done better.
If the rating is under 10, send the rating with feedback to management.
If the rating is under 6, assign a new different support staff member to be that user's dedicated support staff for the future. However, we still want to be sure management checks and resolves the issue in the meantime, both to (1) make sure the user gets their matter fully resolved and (2) so the staff member who provided the allegedly poor support can be coached and trained so they can provide better support in the future. The point of assigning a new dedicated support specialist isn't to have them deal with the current unresolved problem, but rather for if and when the same user has a totally different issue in the future.
The full implementation of the above suggestion will require first completing the below suggestion: