Innovations often combine several components to achieve outcomes greater than the “sum of the parts.” We argue that such combination innovations can introduce an understudied inefficiency—a positive market expansion externality that benefits the owners of the components. We demonstrate the importance of this externality in the market for pharmaceutical cancer treatments, where drug combination therapies have proven highly effective. Using data on clinical trial investments, we document several facts consistent with inefficiently low private innovation: firms are less likely than publicly funded researchers to trial combinations, firms are less likely to trial combinations including other firms’ drugs than those including their own drugs, and firms often wait to trial combinations including other firms’ drugs until those drugs experience generic entry. Using microdata on drug prices and utilization, we quantify the externalities that arise from new combinations and find that the market expansion externality often dominates the standard negative business stealing externality, suggesting too little innovation in combination therapies. As a result, firms may have incentives to free ride off others’ innovation, which we analyze with a dynamic structural model of innovation decisions. We use the model to design cost-effective policies that advance combination innovation. Redirecting publicly funded innovation toward combinations with high predicted market expansion or consumer surplus spillovers minimizes crowd out of private investments, increasing the rate of combination innovation and total welfare while remaining budget neutral.