I analyze data from a one-year study of plurilingualism across the disciplines in Canadian higher education. I focus on how instructors in different disciplines understand their students' plurilingual practices and how they respond pedagogically to teaching in linguistically diverse classes. I employ the theoretical lenses of plurilingualism and plurilingual competence. Selected data are presented from a broader project, namely, interviews with five instructors teaching linguistically diverse classes in the fields of Linguistics, Literature, and Applied Sciences. Data were analysed around three themes: English as an additional language (EAL) -- institutional backdrop, use of languages in class, and teaching strategies. Participants described classes that were characterised by high degrees of linguistic diversity, in which students frequently communicated in Chinese languages, Punjabi, and Korean. I suggest that instructors' perceptions, as well as their pedagogical responses, were framed by two key factors: pervasive institutional discourses that view students' plurilingualism more in terms of deficit than asset, and the tension between plurilingual process and monolingual product: that is, students using languages other than English during the learning process while they are assessed in monolingual academic English.