Conflicts of competences are ubiquitous in law. They represent a serious challenge, in particular, to global constitutionalism and institutional cosmopolitanism. This article argues from a participant’s perspective, following a normative-analytical approach. It develops new taxonomy of competence conflicts. In essence it defends a flexible legal solution to competence conflicts that is inspired by the idea of practical institutional concordance and provides a middle way between strict legal solutions and political appeals for dialogue. Legal authority beyond the state and competence admit of degrees and variability, depending on the legal and factual circumstances of the case at issue. This understanding is enabled by interpreting competences as formal principles. Drawing on research by Alexy and Kumm the details of balancing competences as a distinct legal method are elaborated, using a triadic scale and various factors for determining the concrete weight of a competence. The theory of balancing competences is then applied to the example of competence conflicts in the multilevel system of fundamental rights protection in the EU. In result, a universal but case-sensitive theory is presented that optimally combines flexibility and stability and allows for a pluralist understanding of sovereignty. Institutional cosmopolitanism is thus defended against sceptical pluralism.