Modern markets are increasingly international, online and unrestricted by geographic borders and territoriality. Competition regulation remains decidedly domestic in nature, restrained by principles of jurisdiction and state sovereignty in a way that multinational business is not. With the rise of online markets and transnational trade, legislators and regulators are increasingly expected to grapple with abuses of dominance which span multiple jurisdictions. However, traditional approaches to state sovereignty and prescriptive jurisdiction present fundamental challenges to the effective implementation of competition policy in these modern markets. In particular, abuses of dominance by international or online firms have the potential to profoundly impact national economies. Yet unlike other competition ills, such as cartels, abuse of dominance is not the subject of widespread international regulatory cooperation or legislative uniformity. Against this background, substantive convergence emerges as a potential solution to jurisdictional clash but, as this article explores, it faces legal, sociopolitical, and practical obstacles that make its success not only unlikely, but not necessarily desirable. While recognising the unique political context of the EU legal system, in particular the role of market integration and its place at the core of policy decisions, this article explores what practical guidance may be found in the EU competition law framework. It explores EU horizontal, administrative measures which could be repurposed in order to bring further predictability and clarity to international jurisdictional issues. It concludes by proposing that EU approaches to case allocation, horizontal best practice standards and peer review may be meaningfully adapted by the international competition law community, in order to alleviate jurisdictional issues in competition regulation.