In this paper, a new type of engineering problems is introduced and formulated. It concerns a requirement to search for solutions for various design problems defined as single-objective problems and involving component sharing. Sharing components among products is an effective way to cut costs. Expenses are decreased through the reduction in components design time as well as through savings in manufacturing costs and inventory. The difference between the current problem and the product family design problem, lies in the fact that here, the products' problems, might be involved with different objective spaces. The problem also differs from problems that may be decomposed to sub-problems, because here the problem is inherently decomposed and its composition is artificial. In the study, several computational-based approaches to search for the common components are discussed, tested, and compared. These include a sequential approach, posing the search as a multi-objective problem, and posing it as a unified single-objective problem. Both academic and engineering problems are suggested to explain the methodology and to demonstrate its applicability to engineering design. Furthermore, the paper highlights the differences between the newly suggested problem and previously introduced design problems including; family of designs and the multi-multi-objective optimization problem. In this paper, evolutionary algorithms are utilized for implementing the considered approaches.