Sustainable Development Goals are intrinsically competing, and their embedding into urban systems furthermore emphasises such compromises.When observed at the scale of systems of cities, such concern is considered as a Mains Block Cover series of innovations that challenges the adaptive capacity of urban systems.The spatial complexity, the non-optimal nature of such systems, and the multi-objective aspects of their agents, are among the reasons that raise difficulties when trying to adjust local policies through promoting innovation in order to satisfy at least a couple of SDGs simultaneously.As we lack enough empirical evidence, we propose in this paper to use a stylised simulation model for systems ORG STEEL CUT OATS of cities, focused on innovation diffusion and population dynamics, to show how trade-offs may operate at such a scale.We proceed in particular to a bi-objective optimisation of emissions and innovation utilities, and show that no single urban optimum exists, but a diversity of regimes forming a compromise between the two objectives.