Globally, the purpose of education is becoming increasingly narrowly defined. In this context, this article proposes that supplementary schooling offers a resource for re-thinking the epistemologies and processes of schooling. Drawing on Derrida's notion of "the supplement", the nature and status of this under-researched and marginal sector is interrogated from a historical perspective. Our primary focus is on educational settings established by adults from Black and minority ethnic communities in urban environments in England, which are typically focused on (and societally marked by their attention to) "language", "culture", "heritage", "identity" and, sometimes, "extra tuition". Drawing on exploratory meetings held with key players and conferences, as well as some informal observations in schools, alongside a review of international literature, we highlight the role of theory in posing "better" questions about this disparate, yet vital, sector. Specifically, we discuss how the supplementary status of these schools is produced from the outset, rather than added later, such that the designation "supplementary" fails to specify its precise relationship with formal, mainstream schooling. "Supplementary" emerges as fundamentally ambiguous, and -- within dominant discourse -- as working to suppress sociocultural features of the "mainstream", thereby highlighting the normative and exclusionary character of that mainstream. Two key issues emerge from this analysis: first, that the few commonalities across supplementary schooling provision may arise precisely because of its binary relationship with mainstream schooling; and, second, this analysis not only decentres the "settled" status of mainstream schooling, but also opens up for inquiry the diverse forms and functions of the mainstream.