Lack of specialized data makes building a multi-domain neural machine translation tool challenging. Although emerging literature dealing with low resource languages starts to show promising results, most state-of-the-art models used millions of sentences. Today, the majority of multi-domain adaptation techniques are based on complex and sophisticated architectures that are not adapted for real-world applications. So far, no scalable method is performing better than the simple yet effective mixed-finetuning, i.e finetuning a generic model with a mix of all specialized data and generic data. In this paper, we propose a new training pipeline where knowledge distillation and multiple specialized teachers allow us to efficiently finetune a model without adding new costs at inference time. Our experiments demonstrated that our training pipeline allows improving the performance of multi-domain translation over finetuning in configurations with 2, 3, and 4 domains by up to 2 points in BLEU.