N.J. Stat. Ann. § 40:41A-108

An initiative or referendum petition may be amended at any time within 10 days after the notification of insufficiency has been served by the county clerk, by filing a supplementary petition upon additional papers signed and filed as provided in case of an original petition. The county clerk shall, within 5 days after such an amendment is filed, examine the amended petition and, if the petition be still insufficient, he shall file his certificate to that effect in his office and notify the committee of the petitioners of his findings and no further action shall be had on such insufficient petition. The finding of the insufficiency of a petition shall not prejudice the filing of a new petition for the same purpose.