Social stratification arises from disparities in both the range of opportunities available to people and in how people navigate those opportunities. Yet the relative influences of these two dimensions are rarely observed, as most available information is limited to realized actions. We use the case of university admissions in Sweden to overcome this observational problem. Leveraging comprehensive register and archival data, we break down the cumulative impact of access and navigation differences on the production of gender and social background stratification in university programs of study with varying social outcomes. We show that: (1) In the aggregate, social background and gender exhibit significant cumulative and non-interactive influence on the array of attainable programs, favoring women and individuals from higher social-class backgrounds (2) There is a strong and interactive effect of gender and parents’ SES on the distribution of outcomes of reachable programs (2a) an increase in SES quintile has a systematically positive effect on the median social outcome for each gender, but the spread of this effect between the first and last quintile is twice larger among men than among women (2b) While there is a very large difference between the median social outcome of lower SES quintile of men and women, in favor of women, there is no difference between men and women of the highest SES quintile (3) The number of reachable programs explain most of the difference between applicants and non-applicants, as well as the difference between successful and non successful applicants (4) Net of the space of possible outcome, men of all SES quintiles navigate their possibilities towards higher social outcomes programs than women of all SES, with little to no secondary effect of SES, except for women of the highest quintile outperforming females from the lowest ones in the navigation of their possibles.