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Video has become an integral part of the Internet user content. The use of High Definition (HD) video content increases the bandwidth requirements of the Internet infrastructure. Moreover, rapid increase in the Over-the-Top (OTT) Internet video bandwidth consumption has major impact on the business models of the Internet Service Providers (ISP). To support the ever-growing demand for IP-based video, two major technologies are used: Peer-to-Peer (P2P) for live video and Multi-Layer Cache (MLC) for fully-stored video content. In this paper we focus on partial streaming, which is a `semi-live' form of video delivery of live events such as sports, concerts, and news in the Video-on-Demand (VOD) format. The VOD supports user control features such as Start Over, Pause, Rewind, and Forward. We suggest a new framework for optimizing partial streaming using MLC, which allows storing partial video content in the time-based chunks of data (that is, data packets) while forwarding these data chunks to the users at various levels of ISP networks. The suggested framework may be helpful for solving the OTT bottleneck caused be video streaming.