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Multi-omics has the promise to provide a detailed molecular picture of biological systems. Although obtaining multi-omics data is relatively easy, methods that analyze such data have been lagging. In this paper, we present an algorithm that uses probabilistic graph representations and external knowledge to perform optimal structure learning and deduce a multifarious interaction network for multi-omics data from a bacterial community. Kefir grain, a microbial community that ferments milk and creates kefir, represents a self-renewing, stable, natural microbial community. Kefir has been shown to have a wide range of health benefits. We obtained a controlled bacterial community using the two most abundant and well-studied species in kefir grains: Lentilactobacillus kefiri and Lactobacillus kefiranofaciens. We applied growth temperatures of 30 °C and 37 °C and obtained transcriptomic, metabolomic, and proteomic data for the same 20 samples (10 samples per temperature). We obtained a multi-omics interaction network, which generated insights that would not have been possible with single-omics analysis. We identified interactions among transcripts, proteins, and metabolites, suggesting active toxin/antitoxin systems. We also observed multifarious interactions that involved the shikimate pathway. These observations helped explain bacterial adaptation to different stress conditions, co-aggregation, and increased activation of L. kefiranofaciens at 37 °C.