The board may consider, under a petition filed under section 12:3-38 of this title, the granting of additional lands under water adjacent to the lands to be covered by any confirmatory lease or grant, provided the petitioner shall have made application for the grant of additional lands in accordance with the requirements of the statutes in force at the date of the petition, to the end that a lease or grant may include not only the lands, title to which is being confirmed, but also additional lands adjacent thereto.

The expressed consideration for such lease or grant shall be the sum total of any additional sum to be paid for the confirmation of previous leases or grants and of the sum agreed to be paid for the new area.