Legal multiplicity in the global realm, and the interface conflicts that ensue from it, are widely thought to have a destabilizing effect, blocking the path towards a more integrated and perhaps constitutionalized global order. While this diagnosis may appear plausible if interface conflicts are seen as snapshots, it is less convincing if we regard them, from a diachronic perspective, as part of social processes that define the relation between different norms over time. This paper works towards such a diachronic account, and it creates a typology of interface conflicts and the actors involved in them which helps to generate expectations about the likelihood that these conflicts result in friction. It then uses two case studies of 'irritative' conflicts at the interface between economic governance and human rights to illustrate the dynamics and consequences of this type of conflict. Both cases appear as instances of prolonged norm contestation which, despite continued irresolution of the underlying conflicts as a matter of law, have resulted in a significant reorientation and (partial) consolidation around new interpretations. This suggests that interface conflicts can fruitfully be seen as a pathway for change in the otherwise rigid structure of international law.