The Common European Framework of Reference: Learning, teaching, assessment for Languages (henceforth CEFR) may be said to have been received with as much enthusiasm as defiance. On the one hand, it plays a harmonising role by setting a number of “competencies (knowledge, skills, attitudes) which language users build up in the course of their experience of language use and which enable them to meet the challenges of communication across language and cultural boundaries (...).” (CEFR xii) On the other hand, it purports to promote diversity in various aspects: -diversity of languages with the promotion of plurilingualism, -diversity of methods with its non-dogmatic approach, -diversity of users (learners, teachers, exam makers) even encouraging a critical reading : “As a user, you are invited to use the scaling system and associated descriptors critically.” (CEFR xiii) Does that mean that the CEFR is pursuing contradictory objectives? One of uniting practices and references to language proficiency in Europe, and one of encouraging differences, particularities, and individualities? When one comes across a project based on the framework and aiming at improving teaching practices in European countries, what should one have in mind: unity or diversity, common understanding or specific considerations? What role does intercultural communication play among teachers and teacher trainers striving to make the best use of the CEFR and improve their practices? This article will refer to three European projects which I took part in (the Dutch CEFR grid and EBAFLS) or coordinated (CEF-ESTIM) and compare them to a theoretical frame on the concept of the intercultural. How can people from different countries, from different teaching or testing cultures, work together efficiently using the same tool? What is at stake? What might be the outcome? After a short description of the three projects, we will point at the limits of the intercultural in each of them. Then, we will reflect on the required conditions to develop intercultural behaviour among foreign language teachers. Finally, we will consider whether the need for common understanding should not prevail over the need for being different or if, as Edgar Morin puts it, Europe can be anything but “a Complex”.