We study the allocation of homogeneous positions under affirmative action policies where some positions are reserved for underrepresented groups on a “minimum guarantee” basis. Each individual has a merit-based score and may be eligible for multiple reserves. When an individual counts towards each of the reserves that she is eligible for upon admission, we propose a choice function that satisfies three properties: the minimum guarantee requirement, non-wastefulness, and a stronger fairness notion than the one introduced by Sönmez and Yenmez (2019). Our proposed choice function is the unique one that produces an assignment achieving the maximal cutoff score in a recursive way among all non-wasteful assignments satisfying the minimum guarantee requirement. We show that the outcome of this choice function is not score-wise dominated by any other assignment that satisfies the minimum guarantee requirement.