This study examines how tensions arising from business model innovation (BMI) are managed within a social purpose organisation (SPO) network. We utilise a case study to illustrate how tensions within a network with a dual (social and economic) mission focus, present themselves at three key stages of BMI (initiation, exploration, and exploitation). Moreover, we use illustrative examples to show how network tensions are managed through dynamic capabilities (sensing, seizing, and transformational). The findings show that while engaging in BMI can improve the competitiveness of SPOs, the tensions emerging from a dual mission focus in a multi-stakeholder network are complex, which need to be addressed by careful and nuanced planning in practice. Furthermore, different dynamic capabilities may mediate the effect of tensions and thus help SPO networks to be more effective at different stages of BMI and accomplish a dual mission.