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We consider streaming multiple video assets over a shared backbone network through an intermediate proxy-server to a set of receiving clients. The proxy is located at the junction of the backbone network and the last hop to each of the clients and coordinates the delivery of the videos from the origin media server to the clients. We propose an optimization framework that enables the proxy to coordinate the streaming process such that the overall end-to-end performance of the video streams is maximized for the given data rate resources on the backbone and the last hop links. Prospective video quality requirements for the associated media sessions are also taken into consideration in the analysis. We study in detail the operation of the framework and the influence of the various constraints that it considers through experiments. Furthermore, we measure its performance gains relative to a sender-driven system where the media server controls the delivery of the data with no assistance from an intervening proxy. We establish an analytical relationship between the relative improvement of the proxy-based system, the network conditions on the backbone and the last hops, and the number of streams served. The gains of the proxy-driven system measured in our experiments match closely their expected values predicted by this relationship.