In this paper, we map out the CoCe design space - a design space for co-located collaborative games that use multi-display composition. The design space grew out of the analysis of game instances based on the 4in1 concept. First, we did a horizontal analysis of 16 game instances with 31 corresponding gameplay design patterns (GDP), followed by a vertical analysis of 89 GDPs occurring in the description of the GDP Cooperation. Through inductive analysis, we have identified four perspectives with corresponding dimensions that span the CoCe design space. By applying the CoCe design space with game instances, we illustrate how it can be used both as an analytic tool for analysis of games and also as a generative tool in the design or re-design of cooperative games that use multi-display composition.