This paper aims to provide a tentative roadmap for ensuring that higher education policy makers and practitioners are apprised of what might be done to advance a concept of socially just assessment praxis. It extends current thinking around the notion of social justice approaches to assessment by further developing the conceptual framework proposed in McArthur's recent work (2016). It does so by extending understandings of how a socially just perspective might be realised. Drawing upon recent conceptual developments within both Universal Design for Learning (UDL) and Culturally Sustaining Pedagogy (CSP), the paper proposes a typology for praxis and organisational change. Crucially, this typology focuses upon enhancing learning outcomes for all learners, but it is particularly concerned with enhancing educational experiences and learning outcomes for students that have been systematically marginalised by the normative procedural practices that have traditionally informed the nature of supposedly objective assessment.