Social media platforms, as a particular species of digital platforms offering multiple online services and electronic commerce opportunities, have been under increasing scrutiny by competition enforcement agencies in recent years for engaging in allegedly anticompetitive practices. These technology giants have also come under fire for their role in facilitating various anti-social practices that have sowed societal discord and conflict in many different jurisdictions. In this paper, we examine the reasons why undertakings operating in this particular sector of the digital economy have managed to acquire such an exceptional species of "digital dominance" that makes them particularly challenging targets for competition authorities to rein in using conventional competition law frameworks. We then argue that, in light of the conceptual and practical difficulties of relying on competition law enforcement as the primary mechanism to address the problems associated with the behaviour of social media platforms, policymakers should focus their attention instead on tailor-making sector-specific ex ante regulatory frameworks that are better equipped to address the different public and private interests that need to be balanced against each other when evaluating the conduct of these particular digital ecosystems.