Techniques for multi-target domain adaptation (MTDA) seek to adapt a recognition model such that it can generalize well across multiple target domains. While several successful techniques have been proposed for unsupervised single-target domain adaptation (STDA) in object detection, adapting a model to multiple target domains using unlabeled image data remains a challenging and largely unexplored problem. Key challenges include the lack of bounding box annotations for target data, knowledge corruption, and the growing resource requirements needed to train accurate deep detection models. The later requirements are augmented by the need to retraining a model with previous-learned target data when adapting to each new target domain. Currently, the only MTDA technique in literature for object detection relies on distillation with a duplicated model to avoid knowledge corruption but does not leverage the source-target feature alignment after UDA. To address these challenges, we propose a new Incremental MTDA technique for object detection that can adapt a detector to multiple target domains, one at a time, without having to retain data of previously-learned target domains. Instead of distillation, our technique efficiently transfers source images to a joint target domains' space, on the fly, thereby preserving knowledge during incremental MTDA. Using adversarial training, our Domain Transfer Module (DTM) is optimized to trick the domain classifiers into classifying source images as though transferred into the target domain, thus allowing the DTM to generate samples close to a joint distribution of target domains.Our proposed technique is validated on different MTDA detection benchmarks, and results show it improving accuracy across multiple domains, despite the considerable reduction in complexity. Our code is available at: link 1