Open-set face recognition characterizes a scenario where unknown individuals, unseen during the training and enrollment stages, appear on operation time. This work concentrates on watchlists, an open-set task that is expected to operate at a low False Positive Identification Rate and generally includes only a few enrollment samples per identity. We introduce a compact adapter network that benefits from additional negative face images when combined with distinct cost functions, such as Objectosphere Loss (OS) and the proposed Maximal Entropy Loss (MEL). MEL modifies the traditional Cross-Entropy loss in favor of increasing the entropy for negative samples and attaches a penalty to known target classes in pursuance of gallery specialization. The proposed approach adopts pre-trained deep neural networks (DNNs) for face recognition as feature extractors. Then, the adapter network takes deep feature representations and acts as a substitute for the output layer of the pre-trained DNN in exchange for an agile domain adaptation. Promising results have been achieved following open-set protocols for three different datasets: LFW, IJB-C, and UCCS as well as state-of-the-art performance when supplementary negative data is properly selected to fine-tune the adapter network.