Many people from non-dominant backgrounds or believers from various religions want their children to acquire the best modern knowledge and to remain open to their home cultures and beliefs. However, this double aspiration poses complex challenges, and most scholars have either stressed the importance of addressing identity (and diversity) issues, or claimed that the key is to give everyone access to powerful knowledge. Beginning from curriculum studies' alleged crisis and its relation to this dichotomy, this paper suggests that bridging concern for diverse identities and access to powerful knowledge implies devising curricula that allow for issues that are transversal to the disciplines without collapsing the boundaries between them. Since this has been generally difficult to develop, the paper reflects on the kind of curriculum integration that is needed, arriving at the idea of "interstitial curriculum" or "connective tissue" amid the disciplines. Subsequently, unique features of the "International Baccalaureate Diploma Program" (IBDP) are presented to exemplify these "curricular interstices," and how they help to deal with the epistemological challenges posed by the initially mentioned double aspiration of many families at present.