The engineering of advanced multicellular behaviors, such as the programmed growth of biofilms or tissues, requires cells to communicate multiple aspects of physiological information. Unfortunately, few cell-cell communication systems have been developed for synthetic biology. In this work, I engineer a genetically-encoded channel selector device that enables a single communication system to transmit two separate intercellular conversations. My design comprises multiplexer and demultiplexer sub-circuits constructed from a total of 12 CRISPRi-based transcriptional logic gates, an acyl homoserine lactone-based communication module, and three inducible promoters that enable small molecule control over the conversations. Experimentally-parameterized mathematical models of the sub-components predict the steady state and dynamical performance of the full system. Multiplexed cell-cell communication has applications in synthetic development, metabolic engineering, and other areas requiring the coordination of multiple pathways amongst a community of cells.