We develop a theory of tax reforms for a setting with multi-dimensional heterogeneity amongst taxpayers and multiple economic decisions that are all subject to fixed and variable costs. The theorems in this paper provide a complete characterization of the conditions under which Pareto- or welfare-improving tax reforms exist. We focus on one application, the taxation of couples, and present a detailed analysis of the behavioral responses to taxation in this setting. Squaring the theorems with this analysis yields sufficient statistics for the existence of Pareto- or welfare-improving tax reforms. In the empirical part, we apply them to US data. Our findings include the following: Tax rates on secondary earnings are inefficiently high when secondary earnings are close to primary earnings. Also, reducing the tax system’s degree of jointness is not Pareto-improving. Whether it raises welfare depends on a trade-off between poverty alleviation and gender balance.