While the issue of platform power has received significant attention in academic and policy circles, its concerns have so far been addressed in a piecemeal regulatory fashion. In an effort to bring together different lines of thinking, we create an overarching typology of platform power consisting of three forms of control that can be distinguished from a legal and policy perspective: (1) power over markets; (2) power over individuals; and (3) power over society. The power over markets refers to the impact of platforms on competition and innovation. The power over individuals refers to the impact of platforms on the interests of workers, business users and consumers. The power over society refers to the impact of platforms on politics and opinion formation, and to their presence in an increasing range of spheres of our lives, including domains such as health and education that used to be dominated by public actors. Based on this three-fold characterization, we analyse to what extent the EU regulatory framework is capable of controlling platform power. We conclude that despite the various legislative instruments adopted in recent years, there are still gaps. These gaps are both institutional (lengthy and complex enforcement procedures) and substantive (relatively limited attention to platform power over society). As an alternative to adopting additional legislative instruments for the remaining concerns, we suggest considering consolidating protections substantively (by bringing together rules relevant to platforms in a more focused regulatory framework) and/or institutionally (by giving enforcement powers over platforms to a single regulator).