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Background Identification of complex multidimensional interaction patterns within microbial communities is the key to understand, modulate, and design beneficial microbiomes. Every community has members that fulfill an essential function affecting multiple other community members through secondary metabolism. Since microbial community members are often simultaneously involved in multiple relations, not all interaction patterns for such microorganisms are expected to exhibit a visually uninterrupted pattern. As a result, such relations cannot be detected using traditional correlation, mutual information, principal coordinate analysis, or covariation-based network inference approaches. Results We present a novel pattern-specific method to quantify the strength and estimate the statistical significance of two-dimensional co-presence, co-exclusion, and one-way relation patterns between abundance profiles of two organisms as well as extend this approach to allow search and visualize three-, four-, and higher dimensional patterns. The proposed approach has been tested using 2380 microbiome samples from the Human Microbiome Project resulting in body site-specific networks of statistically significant 2D patterns as well as revealed the presence of 3D patterns in the Human Microbiome Project data. Conclusions The presented study suggested that search for Boolean patterns in the microbial abundance data needs to be pattern specific. The reported presence of multidimensional patterns (which cannot be reduced to a combination of two-dimensional patterns) suggests that multidimensional (multi-organism) relations may play important roles in the organization of microbial communities, and their detection (and appropriate visualization) may lead to a deeper understanding of the organization and dynamics of microbial communities.