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We consider a problem of managing separate multicast sessions from a single transmitter. Each of K sessions has an associated packet stream, and a single transmitter must transmit these packet streams to a group of receivers. The multicast sessions are separate in the sense that each receiver only wants packets from one of the K streams. We will compare the maximum stable arrival rates that can be supported with and without using random linear coding across the K sessions. Intuitively, it seems that coding across sessions is not beneficial. Coding across sessions appears to introduce unnecessary additional delay since each receiver does not receive its next packet until it can decode the head-of-line packets from all K streams. However, we show that in many cases the maximum stable arrival rate that can be supported when coding across sessions is significantly greater than maximum stable arrival rate that can be supported when not coding across sessions. We provide a sufficient condition that indicates when coding across sessions is preferable. This condition is expressed in terms of the number of sessions, the number of receivers per session, and the reliability of the channels connecting the transmitter to the receivers.