Outsourcing the production of selected components to competitors is becoming more common among original brand manufacturers (OBMs); however, OBMs’ increased attention to outsourcing and the growing demand in many markets can result in capacity allocation conflicts for the contract manufacturers. In this study, we consider a scenario in which the OBM decides whether to outsource to a third‐party supplier or to a competitive contract manufacturer (CCM) who has the option of producing a competing product and also has limited capacity. This setting consists of two levels of competition: competition in the component market between the CCM and the spot market, and competition in the final‐product market between the OBM and the CCM. The CCM first chooses the wholesale price and decides whether or not to sell a competing product to the customers. Next, the OBM decides the proportion of its component demand to outsource to the CCM, and then firms set the retail prices. We are interested in investigating the impacts of the CCM's capacity and the impacts of these two levels of competition. We show that the OBM might multisource its component demand only when competition in the final‐product market is intense. We also find that when the CCM's capacity increases, demand may decrease, while the retail price may increase. Moreover, the CCM can be worse off from having more capacity, even when the CCM's capacity is available for free. Our results also show that demand may increase when competition in the final‐product market becomes more intense. Finally, we find that the value of having a third‐party supplier to produce the component decreases amid the intensity of competition in the final‐product market.