The website of Students for Fair Admissions mentions Title VI of the Civil Rights Act.

This brings to mind two recent cases:

Originally Posted by NYT article, 2016 (Texas case)
... the ruling’s basic message was that admissions officials may continue to consider race as one factor among many in ensuring a diverse student body.

Originally Posted by Cornell summary (Michigan case)
Equal Protection Clause does not prohibit the Law School’s narrowly tailored use of race in admissions decisions to further a compelling interest in obtaining the educational benefits that flow from a diverse student body.

Also from Cornell summary:
Originally Posted by Cornell summary (Michigan case)
“It would be a sad day indeed, were America to become a quota-ridden society, with each identifiable minority assigned proportional representation in every desirable walk of life. But that is not the rationale for programs of preferential treatment; the acid test of their justification will be their efficacy in eliminating the need for any racial or ethnic preferences at all”