If, on or before July 1, 1977, a district has assumed the responsibilities, rights, duties, assets, liabilities, and obligations of a sanitary district, the board may, and from time to time thereafter may, increase the number of directors to serve thereon to seven, nine or eleven. The additional directors shall be elected at the next general district election or at a special election called for that purpose. One-half of the additional directors shall hold office until the election and qualification of their successors at the first succeeding general district election, and the other one-half of the additional directors shall hold office until the election and qualification of their successors at the second succeeding general district election. The additional directors shall classify themselves by lot to determine their initial terms of office. Thereafter, they shall hold office for the term provided in Section 30502.