What would be the governance implications if the introduction of the concept of network were to be made a technical-legal category of private international law? The idea behind the present contribution is an attempt to provide an alternative analysis, with technical purchase, which might in turn open the path towards a new pattern of jurisprudence in line with a global legal paradigm in three concrete instances which point to obvious inadequacies in the legal treatment of transnational private power (risk allocation between a parent company and its foreign subsidiary in respect of the conduct of the latter; transnational supply or value chains; and international commercial and investment arbitration). However technical the proposed change might appear, whether or not legal innovation is worthwhile on this point is ultimately a political assessment of the need for balance, responsibility and accountability in global governance.