The prevalence of multimorbid patients (i.e., one person with two or more diseases) is critical for patients, medical doctors, and society alike since it complicates treatment and results in high (treatment) costs. However, contemporary medicine mainly specializes in single-organ approaches, frequently overlooking the interactions between different organs causing multimorbidities. Recent research on bilateral organ crosstalk (OCT) reveals the complex interplay between organs and the importance of studying OCT, especially involving more than two organs. Tackling the challenges associated with multi-organ crosstalk requires fundamental methodological advances in computer science, specifically related to handling multi-modal data, the combinatorial explosion of complexity, and data sensitivity. Thus, research should generally be directed toward (i) methods for identifying affected organs, (ii) concepts for discovering disease progression, and (iii) models for validation in clinical studies. When addressing these challenges interdisciplinarily, computer science and medicine will jointly improve the understanding of OCT and multimorbidity, resulting in novel treatment options for multimorbid patients, reduced healthcare costs, and broad benefits for society.