Worldwide participation in higher education now includes one-third of the age cohort and is growing at an unprecedented rate. The tendency to rapid growth, leading towards high participation systems (HPS), has spread to most middle-income and some low-income countries. Though expansion of higher education requires threshold development of the state and the middle class, it is primarily powered not by economic growth but by the ambitions of families to advance or maintain social position. However, expansion is mostly not accompanied by more equal social access to elite institutions. The quality of mass higher education is often problematic. Societies vary in the extent of upward social mobility from low-socio-economic-status backgrounds. The paper explores the intersection between stratified social backgrounds and the stratifying structures in HPS. These differentiating structures include public/private distinctions in schooling and higher education, different fields of study, binary systems and tiered hierarchies of institutions, the vertical "stretching" of stratification in competitive HPS, and the unequalising effects of tuition. Larger social inequalities set limits on what education can achieve. Countries with high mobility sustain a consensus about social equality, and value rigorous and autonomous systems of learning, assessment and selection in education.