The Board, by the affirmative vote of supervisors representing at least two-thirds of all votes entitled to be cast on behalf of all members and comprising at least two-thirds of all possible supervisors (including vacancies), may authorize the inclusion of additional municipalities in the District upon such terms and conditions as it shall deem to be fair, reasonable and in the best interests of the District. The petitioning municipality shall comply thereafter with the approval procedures specified in 24 V.S.A. chapter 121 (Intermunicipal Cooperation and Services). If a majority of the voters of the petitioning municipality present and voting at a meeting of such municipality duly warned for such purpose shall vote to approve the agreement and the terms and conditions for admission, the vote shall be certified by the clerk of that municipality to the Clerk of the District, and the municipality shall be a member.