Despite rich literature on fairness, relatively little attention has been paid to remediating complex compositional systems built on multi-label classifiers, with respect to many groups, to achieve equality of opportunity. In this paper, we first show that baseline approaches scale linearly with the product of number of remediated groups and the number of prediction labels, making them intractable in practice. We introduce two simple techniques to achieve a constant scaling in this multi-group multi-label setup. We report experimental results in academic and real-world environments to empirically demonstrate the effectiveness of our proposal at mitigation in this setup.