Across all education levels, policymakers are using the re-sorting of students to diversify the socioeconomic composition of student bodies. We study how these integration policies interact, using a heterogeneous agent overlapping generations model featuring multiple periods of human capital development. Households sort into public schools through housing location, and into college via a competitive admissions process. Quality of schools and colleges are endogenous through peer effects. At the public school level, we simulate an integration policy that randomly shifts students across schools. For college, we consider an income-based affirmative action policy. Public school integration weakens the link between residential location and school quality, increasing intergenerational mobility by 2.5%. On the other hand, the college policy decreases intergenerational mobility by 0.7%: when the high-quality college reserves seats for low-income students, it makes college more competitive, which increases sorting at the public school level. In fact, an integration policy that combines public school re-sorting and college affirmative action leads to minimal changes in upwards mobility.