The relative lack of students studying post-compulsory STEM (Science, Technology, Engineering and Mathematics) subjects is a key policy concern. A particular issue is the disparities in uptake by students' family background, gender and ethnicity. It remains unclear whether the relationship between student characteristics and choice can be explained by academic disparities, and whether students' background, gender and ethnicity interact in determining university subject choices, rather than simply having additive effects. I use data from more than 4000 students in England from "Next Steps" (previously the LSYPE) and logistic regression methods to explore the interacting relationships between student characteristics and subject choice. There are four main findings of this study. Firstly, disparities by students' ethnicity are shown to increase when controlling for prior attainment. Secondly, family background indicators are differentially related to uptake for male and female students, with parents' social class and education larger predictors of choice than financial resources. Thirdly, gender, ethnicity and family background interact in determining choices. Particularly, as socio-economic position increases, young women are more likely to choose STEM over other high-return subjects. Finally, associations between student characteristics and subject choices, including interactions, largely persisted when accounting for A-level choices. Implications for policy and future research are discussed.