The production process of metals such as copper, lead, and zinc is characterized by mutual interconnections and interdependence, as well as by the occurrence of a large number of byproducts, which include precious or rare metals, such as gold, silver, bismuth, and indium. On the basis of the framework of waste input-output (WIO), we present a hybrid 10 model that takes full account of the mutual interdependence among the metal production processes and the interdependence between them and all the other production sectors of the economy as well. The combination of a comprehensive representation of the whole national economy and the introduction of process knowledge of metal production allows for a detailed analysis of different materials-use scenarios under the consideration of full supply chain effects. For illustration, a hypothetical case study of the introduction of lead-free solder involving the production of silver as a byproduct of copper and lead smelting processes was developed and implemented using Japanese data. To meet the increased demand for the recovery and recycling of silver resources from end-of-life products, the final destination of metal silver in terms of products and user categories was estimated, and the target components with the highest silver concentration were identified.