An increasing number of companies design a family of product variants simultaneously in order to introduce adequate product variety in the competitive market in a cost-effective way while shortening product lead-times, instead of designing one product at a time. The key to using this approach successfully is to achieve the right trade-offs between product family commonality and performance of individual product variants. This paper considers multi-level commonality in product family design in the sense that the feature or component can be common only among some product variants. This differs from the two extremes of being totally common throughout the family or being completely different from one product variant to another. A product family design model is proposed as a multiobjective optimization. A commonality index is introduced to evaluate the family commonality in the presence of multiple levels. A multiobjective cooperative coevolutionary algorithm is developed for simultaneous design of a family of product variants. Optimal decisions include which design variables should be common among which product variants. Computational experiments are conducted using the design of a family of welded beams to demonstrate the effectiveness of the product family design method proposed in this paper.