Historically, much of the focus of universities, policymakers and governments on higher education's impact on social mobility has been on disadvantaged students' access or admission to university, while focus on such students' successful participation and attainment is growing. The third phase beyond access and participation -- disadvantaged individuals' success beyond graduation -- has often been overlooked in comparison. Within the wider public debate about graduate outcomes, however, it is important that sufficient attention is paid to the specific challenges faced by disadvantaged students in building the skills and individual attributes often most valued -- and in some cases demanded -- by employers. For universities and employers, working to address these challenges can be complicated by narrow definitions of what constitutes an individual graduate's success, and indeed in actually defining what is meant by the term 'disadvantaged' and how it is best measured. This discussion paper concerns the influence of socio-economic background on graduate success and explicitly the notion of a 'third phase' of widening opportunity to supplement widening access and the optimisation of academic achievement regardless of socio-economic background.