This paper analyses the purposes of cooperation as they challenge the European governance of higher education. Using Brexit to analyse meanings of "cooperation" and conveying secondary data analysis of ten case studies undertaken in the framework of the exploratory research project titled "Brexit and higher education in the UK and Europe: Towards a cross-country investigation," this study identifies a plurality of meanings of cooperation. These meanings resonate within the scenarios of Europe 2025 traced by the European Commission. In the scenarios (1) "nothing but the single market," (2) "doing less more efficiently," (3) "those who want more do more," the different meanings of cooperation put at risk the future of cooperation driven by academic values and beliefs at the core of the Europeanisation of knowledge policies. Ultimately, the paper underlines that cooperation as a driver of the internationalisation of higher education questions the role of national openness and/or closure in framing shared European interests and the value of international cooperation.