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Insurance markets often feature consumer sorting along both an extensive margin (whether to buy) and an intensive margin (which plan to buy). We present a new graphical theoretical framework that extends the workhorse model to incorporate both selection margins simultaneously. A key insight from our framework is that policies aimed at addressing one margin of selection often involve an economically meaningful trade-off on the other margin in terms of prices, enrollment, and welfare. For example, while a larger penalty for opting to remain uninsured reduces the uninsurance rate, it also tends to lead to unraveling of generous coverage because the newly insured are healthier and sort into less generous plans, driving down the relative prices of those plans. While risk adjustment transfers shift enrollment from lower- to higher-generosity plans, they also sometimes increase the uninsurance rate by raising the prices of less generous plans, which are the entry points into the market. We illustrate these trade-offs in an empirical sufficient statistics approach that is tightly linked to the graphical framework. Using data from Massachusetts, we show that in many policy environments these trade-offs can be empirically meaningful and can cause these policies to have unexpected consequences for overall social welfare.