Starting from the several conceptual and empirical studies about open innovation modes, this paper attempts to integrate them by suggesting a framework which reveals four basic ways to collaborate. Two variables are considered that represent the degree of openness for a company: (i) the number/type of partners with which the company collaborates, briefly labelled as "partner variety"; (ii) the number/type of phases of the innovation process that the company opens to external contributions, briefly labelled as "innovation funnel openness". By crossing these two variables, four basic modes of open innovation are identified: closed innovators, open innovators, specialized collaborators and integrated collaborators. The framework shows its practical validity in an empirical study that is conducted in Italy with the specific aim at verifying whether companies can really be mapped using this framework, i.e. whether the four modes of open innovation can be found in real companies (framework applicability); whether different modes correspond to different companies' strategies, capabilities, organisational and managerial processes (framework explicative power and usefulness). The framework shows that, in some cases, being totally open in innovation activities is not the only and most suitable option, but that different degrees and ways of "openness" can be implemented successfully, as well as the totally closed option.