The Common Council may establish city departments, offices or agencies in addition to those created by this Charter and may prescribe the functions of all departments, offices and agencies provided; however, that there shall be no more than ten department, offices and agencies each of which will be headed by or under the direction or supervision of a single executive who is appointed by and removed by and directly responsible to the Mayor. Committees and boards appointed and selected by the Common Council shall not be included in the above numerical limitations. Those boards and commissions of the city in existence as of the date of the adoption of this Charter shall continue in existence and retain the responsibilities and authority granted to them unless the Common Council by ordinance changes the responsibilities or authority of the boards or commissions.