Methicillin-resistant Staphylococcus aureus (MRSA) can colonize multiple body sites, and carriage is a risk factor for infection. Successful decolonization protocols reduce disease incidence; however, multiple protocols exist, comprising diverse therapies targeting multiple body sites, and the optimal protocol is unclear. Standard methods cannot infer the impact of site-specific components on successful decolonization. Here, we formulate a Bayesian coupled hidden Markov model, which estimates interactions between body sites, quantifies the contribution of each therapy to successful decolonization, and enables predictions of the efficacy of therapy combinations. We applied the model to longitudinal data from a randomized controlled trial (RCT) of an MRSA decolonization protocol consisting of chlorhexidine body and mouthwash and nasal mupirocin. Our findings (i) confirmed nares as a central hub for MRSA colonization and nasal mupirocin as the most crucial therapy and (ii) demonstrated all components contributed significantly to the efficacy of the protocol and the protocol reduced self-inoculation. Finally, we assessed the impact of hypothetical therapy improvements in silico and found that enhancing MRSA clearance at the skin would yield the largest gains. This study demonstrates the use of advanced modelling to go beyond what is typically achieved by RCTs, enabling evidence-based decision-making to streamline clinical protocols.