The TRANSLINGUAM-UNI Project aims to investigate whether multilingual and multicultural undergraduate university classrooms with full English-medium instruction foster the development of transcultural competence among students, and to what extent. A novel contribution includes understanding this competence from an interdisciplinary perspective (educational sociolinguistics, language acquisition, linguistic anthropology and social psychology) and measuring it along four dimensions: (1) linguistic (individual progress in English and translingualism), (2) attitudinal (towards the languages present in the classroom), (3) affective (development or not of intercultural sensitivity) and (4) identitary (development or not of a cosmopolitan identity). The project is an extension of a previous project on linguistic practices and attitudes in secondary school classrooms (FFI2014-52663-P). As in those classrooms, present-day university classrooms foster social networks where, due to international migration and growing academic mobility, young people from different origins co-construct adult attitudes and identities and may develop multilingual skills and intercultural sensitivity. To study the four dimensions, the project will develop a case study of an undergraduate classroom with full English-medium instruction that exemplifies the linguistic and cultural diversity discussed above. We will follow a mixed-methods approach for collecting and analyzing data for the study of linguistic attitudes and practices and identity affiliations. The design will include a control group and a longitudinal component. The understanding of these processes of development of multilingualism and transcultural socialization in such an internationalized educational context and of their consequences will support our transfer objective: the design of a quality certification model for university teaching in English. This certificate (EMICERT) will be part of the internationalization mission of the university and, therefore, of use to those responsible for higher education institutions and their instructors. The ultimate goal of the project will be to provide knowledge and tools to academic and political leaders interested in solving some of the challenges posed to present-day educational systems and in promoting better preparation of young people for multilingual and multicultural academic and professional contexts.