In co-design there seems to be a widespread understanding that innovation is a planned, goal-oriented activity that can be propelled forward through well-facilitated events in which company employees collaborate with external parties (users in particular) and the conversations aim at consensus about new product and service ideas. Conflict belonged to the 'old days' when participatory design played a part in the struggle between workers and management. Based on the theory of complex responsive processes of relating, we suggest a new way of understanding innovation as the emergence of new meaning in - often conflictual - conversations. We argue that the meeting of participants with different stakes is crucial precisely because crossing intentions can create new insight and movement of thought and action. We use improvised theatre to investigate what happens in industrial (and other) organizations that embark on participatory activities, and the barriers that prevent them. By analysing improvised scenes and the way the audience reacts, we characterize the quality of conversations that seems to allow new meaning to emerge and thus stimulates innovation. We suggest that we need to develop new formats of collaboration for large, complex contingents of stakeholders, where conflicting intentions are encouraged.