The only way for a regular living person to be moved from Private to some other privacy is for them to pass away, and as Ellen mentioned, update their date of death and change death indicator from "still living" to some other item.
We are in the process of updating living Notables from Private to some other privacy level, and they are a rare exception to the policy regarding living persons. If the person you are wanting to reduce the privacy is a Notable, then they would have to first qualify as a Notable, be accepted by the project, then the project and project leader would as a co-manager of the profile update the privacy level.