A person on a preliminary promotion list who is eligible for veteran’s preference under any law or agreement applicable to an affected department may file a written application for that preference within 10 days after the initial posting of the preliminary promotion list. The veteran’s preference shall be calculated as provided in the applicable law and added to the applicant’s total score on the preliminary promotion list. Any person who has received a promotion from a promotion list on which his or her position was adjusted for veteran’s preference, under this Act or any other law, shall not be eligible for any subsequent veteran’s preference under this Act.