Multi‐level global governance was introduced at the United Nations summit in Rio in 1992 as a new model to achieve a broad global mobilization of different actors in sustainable development. This model has been extended to climate governance. It has become a global system with its own inherent logic, dynamics and stabilization mechanisms. This article deals with the systemic dimension (the architecture) of global multi‐level climate governance across levels and sectors. It refers to the model and its practical implementation at different levels. The text poses four hypotheses: (1) the global multi‐level system of climate governance can be regarded as a structure which offers opportunities for ambitious innovation‐based climate strategies; (2) each level of the global system has its own specific responsibilities, challenges, opportunities and mechanisms for lesson‐drawing; (3) the main lesson to be learned is to make use of the co‐benefits characteristic to climate mitigation; and (4) the system's multi‐sectoral and multi‐actor structure provides additional opportunities to address such co‐benefits and to mobilize different interests in the pursuit of climate policy objectives. After outlining these hypotheses in more detail, the article will then conclude with a set of policy recommendations. © 2017 The Authors. Environmental Policy and Governance published by ERP Environment and John Wiley & Sons Ltd