Legal multiplicity in the global realm, and the interface conflicts that ensue from it, are widely thought to have a destabilising effect, blocking the path towards a more integrated and perhaps constitutionalised global order. While this diagnosis may appear plausible if interface conflicts are seen as snapshots and rivalrous institutions as the main actors, it is less convincing if we regard these conflicts as part of social processes of contestation that define the relations between different norms over time. It is also less plausible if actors with other orientations – norm irritation or navigation – are taken into view. This article works towards a more encompassing account, both temporally and as regards actor orientations. It uses two case studies of conflicts at the interface between economic governance and human rights to probe the plausibility of its conjectures. 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, rather than destabilising the rule of law, may also open a pathway for change in the otherwise rigid structure of the international legal order.