As shown in Deza et al. [4], for a periodic review Assemble-To-Order (ATO) system that aims to maximize reward, lowering the degree of component commonality may yield a higher Type-II service level. This is achieved via separating inventories of all the shared components for different products. We further study the optimal bill-ofmaterials (BOM) structure for two-product ATO systems with arbitrary number of components. The inventory of a common component can be dedicated or shared between different products. We show that an optimal BOM can be found between the following two extremal configurations: either two products share all common components, or they do not share any common component.