Since the Second World War, global politics has been centred around Western liberal principles. International Organisations (IOs) are guardians of this liberal international order (LIO), ranging from the United Nations to World Trade Organisation, aiming to promote liberal democracy, human rights, rule of law and open markets. Although there has been significant attention to the recent decline of the LIO, this body of work overlooks the key position of IOs in it. In this paper, we study the brokering role of IOs in the field of migration and ask: To what extent do IOs need to broker between competing actors and their competing agendas? With the support of Discourse Network Analysis (DNA), an application of social network analysis (SNA) to policy debates, we map actor coalitions and their proposed policies in the debate on migration to Europe between 2000 and 2020 in a novel dataset of 12,700 coded statements from international press agency reports. Based on Relational Event Models, and a battery of controls based on actor activity and concept popularity, we find that IOs mediate between governments and NGOs as well as their competing agendas such as security interests and human rights in the global migration debate. However, we also show that moments of perceived crisis bring the IOs closer to governments, jeopardising key moral principles of the LIO such as human rights. These findings have important implications for the global governance of migration.