This article conducts a comparative analysis of the American and European Conventions on Human Rights to review the relationship between conventionality control and constitutionality control assumed by domestic courts. First, the analysis negates the monist pyramid model by pointing out the limits of the supremacy of international law and constitution. Given the integration of conventionality control into constitutionality control in practice, this study instead presents the normative framework of the trapezium model, crowning the common values recognized by both national constitutions and international law. This research also contributes to clarifying the principle, a fitting concept to the trapezium schema, focusing on the most favourable treatment for individuals. Specifically, it proves the principle’s double function to offensively pierce or defensively safeguard the boundary between international and domestic legal orders. Finally, it argues that in cases of conflicting rights between different individuals, the principle relativizes an absolute protection of certain rights to strike balance between them. In essence, conventionality control and constitutionality control should be coordinated by the open-minded, substance-oriented, principle within the pluralist trapezium, in lieu of the principle of the closed, formal supremacy of international law or constitution within the monist pyramid.