Serious games are increasingly used at all levels of education. However, research shows that serious games do not always fulfill all the targeted pedagogical objectives. Designing efficient and engaging serious games is a difficult and multidisciplinary process that requires a collaborative approach. Many design frameworks have been described, most of which are dedicated to the development of specific types of serious games and take the collaborative dimension into account only to a limited extent. Our aim was to create a generic serious game design framework that could be adapted to all kinds of serious games and implemented in a collaborative web platform. We combined the results of a literature review with our experience in serious game design and development to determine the basic building blocks of a collaborative design framework. We then organized these building blocks into categories and determined the features that a generic design framework should include. Finally, based on the paradigm of complex systems and systemic modelling, we created the co.LAB generic design framework and specifications to allow its implementation in a collaborative web platform.