Firms can form partial ownership arrangements by purchasing claims to competitor's profits in order to commit to less aggressive competition. These arrangements can increase profits for all firms in the industry even in the absence of synergies. Using a conjectural variations model, we show that with more than two symmetric firms engaged in quantity competition or with more cooperative conjectures, partial ownership arrangements are never individually rational for all participants. Conversely, with conjectures that lead to more rivalrous equilibria than Cournot, there exist individually rational partial ownership arrangements with any number of firms in the industry.