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.