Engineering multicellular consortia, where information processing is distributed across specialized cell types, offers a promising strategy for implementing sophisticated biocomputing systems. However, a major challenge remains in establishing orthogonal intercellular communication, or "wires," within synthetic bacterial consortia. In this study, we address this bottleneck by integrating phagemid-mediated intercellular communication with CRISPR-based gene regulation for multicellular computing in synthetic E. coli consortia. We achieve intercellular communication with high sensitivity by regulating the transfer of single guide RNAs (sgRNAs) encoded on M13 phagemids from sender to receiver cells. Once inside the receiver cells, the transferred sgRNAs mediate gene regulation via CRISPR interference. Leveraging this approach, we successfully constructed one-, two-, and four-input logic gates. Our work expands the toolkit for intercellular communication and paves the way for complex information processing in synthetic microbial consortia, with diverse potential applications, including biocomputing, biosensing, and biomanufacturing.