The research project “Maximizing the integration capacity of the European Union: Lessons and prospects for enlargement and beyond” (MAXCAP) aims to assess the process of EU’s Eastern Enlargement. The leading notion of the 9 renowned European universities and expert organizations is that the assessment of EU’s approach towards the integration of the countries of the Eastern Enlargement has the potential to inform the current enlargement process, including Western Balkan countries and Turkey, who aim at EU accession. This multifaceted assessment can help build a foundation for policy recommendations to improve the integration capacity of the EU in the future. By presenting the research findings as well as opinions and discussions from the international seminar in Sofia, this publication is a continuation of the productive dialogue among academic circles and institutions, which is at the heart of the MAXCAP project. The approaches towards future EU enlargements have to be sensitive to the diverse trajectories of the societies of Eastern and South-Eastern Europe, which are not necessarily only negative, as the debate in Sofia has shown. This calls for innovative research instruments which can register the specificities in the different national cases, including public attitudes towards integration. The texts in this publication are primarily aimed at the solution of this methodological task.