This paper seeks to analyse the policy trajectory of the inter-regional plans to establish a common space in higher education (HE) involving the European Union (EU) and Latin America and the Caribbean (LAC) regions. Although both regions developed different formats of higher education cooperation programmes, it was in 1999 that an institutionalised bi-regional dialogue appeared -- and HE was defined as a strategic partnership. In November 2000, ministers of education on both sides of the Atlantic launched the largest HE project to date: the EU-LAC (ALCUE) HE Common Area, involving 60 HE systems. Understanding (inter-)regional HE policies as an expression of global education policies, I conducted a historical analysis of this inter-regional policy from 2000 until 2018 using Roger Dale's framework of pluri-scalar governance of education. The tracing of the events since 1999 helped unveil the mechanisms of changes in this inter-regional policy. As a result, I was able to differentiate between two moments in the policy process: the ALCUE Project (2000-2008) and the EU-CELAC dialogue (2010-2018). Results point to the defining role of the EU in shaping the inter-regional dialogue in terms of regional mandate and actorness. The research shows that the advent of CELAC as a regional actor in Latin America in 2010 has strengthened the role of the EU in defining the inter-regional HE project.