A critical component in knowledge distillation is the means of coupling the teacher and student. The leading sequence knowledge distillation method involves supervised learning of the student against teacher-decoded synthetic outputs, and is exemplified by the current state of the art, which incorporates minimum Bayes risk(MBR) teacher decoding. In this paper we seek to integrate MBR more tightly in distillation training, specifically by using several high-scoring MBR translations, rather than a single selected sequence, thus capturing a rich diversity of teacheroutputs. This approach enhances the diversity of synthetic training data, without requiring further human inputs or labeled data. Our experiments on English to German and English to Japanese translation show consistent improvements over strong baseline methods for both tasks and with varying model sizes. Additionally, we conduct a detailed analysis focusing on data efficiency and capacity curse aspects to elucidate MBR-n and explore its further potential.