An initiative, referendum, or recall petition may be amended at any time within ten days after the making of a certificate of insufficiency by the city secretary, by filing a supplementary petition upon additional papers signed and filed as provided in case of an original petition. The city secretary shall, within five days after such an amendment is filed, make examination of the amended petition and, if the city secretary’s certificate shall show the petition still to be insufficient, the city secretary shall file it in the city secretary’s office and notify the committee of the petitioners of the 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.