In many English-speaking countries bilingual and multilingual speakers of English are integrated into mainstream classrooms, where the teacher is expected to help them "catch up" with speakers of the dominant language. In this presentation, I argue that we teach in culturally and linguistically diverse societies that are increasingly interconnected through a broadened range of multimodal and digital textual practices. Intuitively, one might expect that multimodal approaches are more equitable than exclusively print-based approaches because learners can draw from a broader range of semiotic resources. Yet the potentials of using multiple modes and new digital media to provide greater access to multiliteracies cannot be assumed. I draw on a case study of a multilingual language learner, Paweni, a Thai immigrant, describing how she and her peers negotiated cultural and linguistic difference. These encounters occur during multiliteracies lessons involving both print and digital texts. I theorise a "dialectic of access" to explain the reciprocal interaction between the agency of learners, modes, and media. I apply Giddens' structuration theory to take into account the social structures - domination, signification, and legitimation - that played an important role in this dialectic of access.