Previous research on classroom interaction in international university contexts tended to focus on individual speakers' language (in)competence. This paper adopts a translanguaging and spatial orientation to intercultural classroom interaction and highlights the role of situated assemblages of linguistic, semiotic and multimodal resources embedded in the environment of learning activities for successful communication. The study provides a close multimodal conversation analysis of the interaction between a Chinese instructor and an international student in a music classroom in an international university adopting English medium in China. The findings illustrate how diverse resources beyond the official language of instruction congregated at a particular time in the classroom, interacted with one another and worked collaboratively to allow the two participants, with language barriers between them, to communicate smoothly and accomplish the teaching/learning tasks efficiently. We thus call for an expanded conceptualization of communicative competence in intercultural (classroom) interaction in international higher education, which moves beyond the linguistic-centered view and incorporates the value of spatial repertoires in generating individuals' situated 'language ability' for achieving communicative, teaching and learning goals. Implications for language policy and pedagogy in international universities are discussed.