For decades, social theorists have posited--and descriptive accounts have shown--that students isolated by both social class and ethnicity suffer extreme deprivations that limit the effectiveness of equal-opportunity interventions. Even educational programs that yield positive results for moderately disadvantaged students may not prove beneficial for those who possess less of the economic, social, and cultural capital that play a critical role in improving educational outcomes. Yet evaluations of school choice and other educational interventions seldom estimate programmatic effects on severely disadvantaged students who are isolated by both ethnicity and social class. We experimentally estimate differential effects of a 1997 New York City school voucher intervention on college attainment for minority students by household income and mother's education. Postsecondary outcomes as of 2017 come from the National Student Clearinghouse. The severely deprived did not benefit from the intervention despite substantial positive effects on college enrollments and degree attainment for the moderately disadvantaged. School choice programs and other interventions or public policies may need to pay greater attention to ensuring that families possess the requisite forms of capital--human, economic, social, and cultural--to realize their intended benefits.