A coalition of Asian-American organizations asked the Department of Education on Monday to investigate Brown University, Dartmouth College and Yale University, alleging they discriminate against Asian-American students during the admissions process.

While the population of college age Asian-Americans has doubled in 20 years and the number of highly qualified Asian-American students “has increased dramatically,” the percentage accepted at most Ivy League colleges has flatlined, according to the complaint. It alleges this is...