The European Higher Education Area (EHEA) constitutes an international regime which attempts to solve intra-European problems, as well as to respond to global challenges. Using the regime complexity approach, this article investigates the external effectiveness of the EHEA, which refers to its ability to play a key-role in the Higher Education (HE) regime complex consisting of overlapping and non-hierarchical institutions governing this area. It is also related to the EHEA capacity to become a co-shaper of an emerging global HE agenda and governance architecture as well as to influence policy outcomes and tools embedded in the world order settings. Taking into consideration the leading role of EU within the EHEA our analysis demonstrates that EHEA/EU employs an interplay management strategy aiming to promote and co-shape the HE global order.