Understanding the dissipation of innovations is necessary to develop them, as a company on its own does not have all the capabilities that it needs. On the contrary, they are increasingly spread over internal and external contexts, and are not developed in isolation. Most of the time, they depend on interactive, innovative processes in a global context. The aim of this study is to evaluate how the global organizational structure of innovation affects the dynamic capability of cooperation (cooperability) in Brazilian multinationals (BMNs). To achieve this goal, we conducted a survey of BMNs, and a final sample of 60 companies answered a structured questionnaire. We performed statistical tests such as Factor Analysis, Cronbach's Alpha, Multiple Regression and Hierarchical Cluster, and cross-analysis of quantitative results that enabled us to create a Cooperability Model, that is, a model of local, international and global development for a dynamic capability of cooperation in BMNs. The results show that technological strengths of foreign subsidiaries and the reverse transfer of their capabilities to the parent company and technology partners affect the dynamics of cooperation in BMNs (inputs and results of cooperability). Furthermore, we detected an inverse relationship between the autonomy of foreign subsidiaries and the dynamic of cooperation in BMNs.