This study examines the equilibrium channel structure strategy in a supply chain where a manufacturer can sell products to consumers via/on an online platform, and firms may focus on both profit and consumer surplus. We consider three supply chain channel structures: a reselling channel (mode R), wherein the platform acts as the reseller; an agency channel (mode A), wherein the platform acts as the marketplace; and a dual channel (mode D), wherein the platform acts as both the reseller and marketplace. This study explores the strategic effect of the dual-purpose concern on the co-opetition relationship of firms and derives ramifications for the optimal channel structure. First, the platform may abandon mode A when the manufacturer’s consumer surplus concern is high, even if the commission rate is high. This is because the manufacturer’s sales revenue may be harmed by the higher selling quantity and lower price resulting from the increased concern of consumer surplus in mode A. The manufacturer prefers mode D (mode R) only when the commission rate is low (high). However, the supply chain may prefer mode R (mode D) when the platform’s consumer surplus concern is high (low) irrespective of the commission rate. Second, with dual-purpose firms, both the platform and manufacturer may prefer mode R (mode D) when the commission rate is medium and the platform’s consumer surplus concern is high (low). Third, mode A is beneficial to consumer surplus and social welfare as long as agency selling is viable, which occurs when the consumer surplus concern and the commission rate are not too high; otherwise, mode D is the optimal choice, because it enables the supply chain to sell products to consumers in a more flexible way. Finally, the results are robust to a parsimonious dual-purpose platform, an imperfect competitive market, price competition with a dominant platform, multiple competing manufacturers, and a non-zero slotting fee.