The aim of this study is to shed light on the ways in which transitions and support are framed in policy contexts in relation to widening participation in higher education (HE) in Sweden and Italy. More specifically, this study investigates the ways in which the discourse about the inclusion of migrant students in HE is framed in relation to the kinds of support for this group offered in two higher educational institutions, in Sweden and Italy. Furthermore, the study sheds light on the ways in which policy ideas about transition and widening participation are enmeshed in the students' narratives and how they affect their experiences of participation, normalization and marginalization in HE. The analysis includes two datasets: (i) national policy, laws and regulations and webpages of a selection of national universities and university colleges; and (ii) ethnographically generated data that builds upon a case-study design and consists of audio recordings of informal discussions and interviews with students. We are, in this study, interested in framing diversity in terms of a move beyond the naturalization of hegemonic stances where labelled "Others" (e.g. based on cultural/ethnic background, functionality, socio-economic status) are treated as essentialized or mutually exclusive categories. One of the central, frontline contributions of this study, lies in its attempts to analytically scrutinise processes of inclusion and marginalisation that include a broad analytical gaze. This allowed us to analyse the mismatch between the range of support provided, and the actual needs and challenges that migrant students meet in their transition and participation to higher education in two European countries.