Numerous methods for time-series anomaly detection (TSAD) have emerged in recent years, most of which are unsupervised and assume that only normal samples are available during the training phase, due to the challenge of obtaining abnormal data in real-world scenarios. Still, limited samples of abnormal data are often available, albeit they are far from representative of all possible anomalies. Supervised methods can be utilized to classify normal and seen anomalies, but they tend to overfit to the seen anomalies present during training, hence, they fail to generalize to unseen anomalies. We propose the first algorithm to address the open-set TSAD problem, called Multivariate Open-Set Time-Series Anomaly Detector (MOSAD), that leverages only a few shots of labeled anomalies during the training phase in order to achieve superior anomaly detection performance compared to both supervised and unsupervised TSAD algorithms. MOSAD is a novel multi-head TSAD framework with a shared representation space and specialized heads, including the Generative head, the Discriminative head, and the Anomaly-Aware Contrastive head. The latter produces a superior representation space for anomaly detection compared to conventional supervised contrastive learning. Extensive experiments on three real-world datasets establish MOSAD as a new state-of-the-art in the TSAD field.