Major carbon-pricing systems in Europe and North America involve multiple jurisdictions (countries or states). Individual jurisdictions often pursue additional Initiatives – such as unilateral carbon price oors, legislation to phase out coal, aviation taxes or support programs for renewable energy – that overlap with the wider carbon-pricing system. We develop a general framework to study how the climate benefit of such overlapping policies depends on their design, location and timing. Some policies leverage additional climate benefits elsewhere in the system while others backfire by raising aggregate emissions. Our model encompasses almost every type of carbon-pricing system used in practice.