In the framework of the Sustainable Development Goals, higher education has been given a key role in addressing societal challenges, reducing poverty, ensuring sustainable livelihoods and protecting the natural environment. Yet there has been a singular lack of imagination as regards the institutional forms that might help support this vision. This article reports on the findings of an exploratory qualitative case study of the Intercultural University of Veracruz, one of a number of institutions created in Mexico to ensure access for indigenous populations, to promote local development and to provide a space for intercultural dialogue. The findings show a number of ways in which this innovative institution provides opportunities for supporting the SDGs that go beyond conventional universities. The university addresses SDG4 by enabling access for marginalised populations, and through its engaged teaching, research and community engagement also contributes to environmental protection, health, livelihoods, gender equality and a range of other goals. However, it also presents challenges to the global framework, highlighting the lack of attention to culture, language, identity and knowledge traditions, and in critiquing the very basis of its conception of development. Implications are drawn out more broadly for the relationship between higher education and international development in the contemporary era.