Can one container make two certificates of origin

Two companies supply for one customer, and now one container. We are one of them. The shipper of the bill of lading is not our company. All the goods should be made a bill of lading to the order of the other party. So we don't have to do the certificate of origin. If I don't do it, will it affect my own verification? If you want to do it, it's just a cabinet to do two certificates of origin. The other party still collects money from L / C. But we don't do the certificate of origin for our part of the goods. Can the customer clear the certificate of origin made by the other company.