Unsupervised domain adaptation (UDA) seeks to alleviate the problem of domain shift between the distribution of unlabeled data from the target domain w.r.t labeled data from source domain. While the single-target domain scenario is well studied in UDA literature, the Multi-Target Domain Adaptation (MTDA) setting remains largely unexplored despite its importance. For instance, in video surveillance, each camera can corresponds to a different viewpoint (target domain). MTDA problem can be addressed by adapting one specialized model per target domain, although this solution is too costly in many applications. It has also been addressed by blending target data for multi-domain adaptation to train a common model, yet this may lead to a reduction in performance. In this paper, we propose a new unsupervised MTDA approach to train a common CNN that can generalize across multiple target domains. Our approach the Multi-Teacher MTDA (MT-MTDA) relies on multi-teacher knowledge distillation (KD) in order to distill target domain knowledge from multiple teachers to a common student. Inspired by a common education scenario, a different target domain is assigned to each teacher model for UDA, and these teachers alternatively distill their knowledge to one common student model. The KD process is performed in a progressive manner, where the student is trained by each teacher on how to perform UDA, instead of directly learning domain adapted features. Finally, instead of directly combining the knowledge from each teacher, MT-MTDA alternates between teachers that distill knowledge in order to preserve the specificity of each target (teacher) when learning to adapt the student. MT-MTDA is compared against state-of-the-art methods on OfficeHome, Office31 and Digits-5 datasets, and empirical results show that our proposed model can provide a considerably higher level of accuracy across multiple target domains.