The promotion of English medium instruction (EMI) in higher education has been a widely adopted institutional response to the forces of globalization in the 21st century. However, while EMI has received much enthusiasm in policy discourse, little research has been conducted to explore whether it effectively addresses the new demands of an increasingly multilingual student body. To fill this gap, in this study I draw on extensive literature on linguistically responsive instruction (LRI) to examine: 1) the practices that are linguistically responsive in higher education EMI classrooms, and 2) the affordances and constraints of such practices. The data for this study -- taken from a larger research project that looked into different instructional outcomes of EMI -- show that approaches to LRI were manifested in three main ways: technical, facilitative, and sociocultural. To illustrate what these labels mean, a close-up look into three classroom profiles and interviews conducted with the lecturers of each of these classes are provided. Importantly, the multiple approaches to LRI pointed toward a common concern that centered on students' English proficiency. While LRI may have helped resolve immediate comprehension issues and low participation in classroom interactions, the increased attention to language in content courses posed a potential threat to the teaching of the subject discipline. This study, therefore, argues that aside from equipping individual lecturers with the knowledge, skills, and dispositions to be linguistically responsive, introducing wider structural changes is also necessary so that different student needs (e.g., linguistic, cultural, academic) can be more sustainably supported.