Signal crosstalk within biological communication networks is common, and such crosstalk can have unexpected consequences for decision making in heterogeneous communities of cells. Here we examined crosstalk within a bacterial community composed of five strains of Bacillus subtilis, with each strain producing a variant of the quorum sensing peptide ComX. In isolation, each strain produced one variant of the ComX signal to induce expression of genes associated with bacterial competence. When strains were combined, a mixture of ComX variants was produced resulting in variable levels of gene expression. To examine gene regulation in mixed communities, we implemented a neural network model. Experimental quantification of asymmetric crosstalk between pairs of strains parametrized the model, enabling the accurate prediction of activity within the full five-strain network. Unlike the single strain system in which quorum sensing activated upon exceeding a threshold concentration of the signal, crosstalk within the five-strain community resulted in multiple community-level quorum sensing states, each with a unique combination of quorum sensing activation among the five strains. Quorum sensing activity of the strains within the community was influenced by the combination and ratio of strains as well as community dynamics. The community-level signaling state was altered through an external signal perturbation, and the output state depended on the timing of the perturbation. Given the ubiquity of signal crosstalk in diverse microbial communities, the application of such neural network models will increase accuracy of predicting activity within microbial consortia and enable new strategies for control and design of bacterial signaling networks.