If it appears to the board that the full capacity of the works built or constructed, or being built or constructed, under an appropriation of water under the Water Commission Act or this code, will not develop the full capacity of the stream at that point, and that the public good requires it, and the board specifically so finds after investigation and hearing of the persons interested, the board may permit any person to repair, improve, add to, supplement, or enlarge, at his own expense, any works already so built or constructed or in process of being so built or constructed under the provisions of this division, and to use the works jointly with the owners thereof.