Many of today's manufacturing companies are using platform-based product development to realize families of products with sufficient variety to meet customers' demands while keeping costs relatively low. Although the benefits of commonality are widely known, many companies are still not taking full advantage of it when developing new products or redesigning existing ones. One reason is the lack of appropriate methods to retrieve and reuse relevant information when re/designing products. In this paper, we propose a framework to (1) collect information on product families, (2) store it using ontology, (3) retrieve relevant information on a product family using graph query, (4) reuse this information to redesign a product family using a genetic algorithm-based optimizer and (5) represent the redesigned product family using a product family concept lattice, which we call a networked bill of material (NBOM). Besides increasing the understanding of the interaction between components in a product family, the framework explicitly captures the redesign process for improving commonality using formal concept analysis. As an example, a family of staplers is redesigned using the proposed framework.