Administrative services such social care, tax reduction, and many others using complex decision processes, request individuals to provide large amounts of private data items, in order to calibrate their proposal to the specific situation of the applicant. This data is subsequently processed and stored by the organization. However, all the requested information is not needed to reach the same decision. We have recently proposed an approach, termed Minimum Exposure, to reduce the quantity of information provided by the users, in order to protect her privacy, reduce processing costs for the organization, and financial lost in the case of a data breach. In this paper, we address the case of decision making processes based on sets of classifiers, typically multi-label classifiers. We propose a practical implementation using state of the art multi-label classifiers, and analyze the effectiveness of our solution on several real multi-label data sets.