We extend recent work on rate-distortion optimized streaming of video to include the case when multiple, independently encoded and packetized versions of the video are available for transmission. While there has been much recent work on the rate-distortion optimized streaming of packetized video, previous work has focussed on layered video encodings and encodings that are comprised of a single set of interdependent packets. In this paper we extend the rate-distortion optimizing packet transmission algorithms, a major benefit of which is that they select the optimal source rate from a rate-scalable encoding on a per-transmission basis, to handle the case of multiple independent encodings, the most ubiquitous form of rate-scalable video in use. In our experimental results, we show up to a 3 dB performance improvement for our multiple-encoding optimizing scheduler over a non-optimizing scheduler.