The European Universities Initiative (EUI), launched in 2019, fosters the development of networks of universities across Europe with the aim of enabling students to obtain a degree by combining studies in several countries and strengthening collaboration in both teaching and research, and by extension, the international competitiveness of European universities. As well as constituting one of the European Commission's most significant policies with respect to higher education, over recent years, the initiative also provides a useful lens to explore how European higher education is understood by a range of social actors. Indeed, drawing on relevant policy documents and interviews with key policy actors, this article examines what broader messages about the European higher education space (actual and ideal) are conveyed by public discussions about EUI networks. The analysis reveals significantly different perspectives about: the geographical boundaries of the European higher education space; the extent to which European higher education should be inclusive and/or aim to promote excellence; whether higher education constitutes a vehicle for further Europeanisation; and the role of nation-states in a changing Europe.