The European Union, a pioneer in gender equality policies, is moving from predominantly attending to gender inequality, towards policies that address multiple inequalities. This article argues that there are tendencies at EU level to assume an unquestioned similarity of inequalities, to fail to address the structural level and to fuel the political competition between inequalities. Based upon a comparison of specific sets of inequalities, this article explores where and how structural and political intersectionality might be relevant. It argues that a (...) ‘one size fits all’ approach to addressing multiple discrimination is based on an incorrect assumption of sameness or equivalence of the social categories connected to inequalities and of the mechanisms and processes that constitute them. Focusing on similarities ignores the differentiated character and dynamics of inequalities. It also overlooks the political dimension of equality goals. Moreover, it has become clear that attention to structural mechanisms and to the role of the state and the private sphere in reproducing inequalities is much needed. The final part of the article presents constructive ideas for a more comprehensive way of addressing multiple inequalities. (shrink)