The executive may: (1) appoint and remove all employees of the local government; (2) appoint and remove, with the consent of a majority of the commission, all employees of the local government; (3) appoint, with the consent of a majority of the commission, all department heads and remove department heads and may appoint and remove all other department employees; or (4) appoint and remove, with the consent of a majority of the commission, all department heads and appoint and remove all other employees of the local government.