Multiplex immunoassays are facilitating the parallel measurement of antibody responses against multiple antigenically-related pathogens, generating a wealth of high-dimensional data which depict complex antibody-antigen relationships. In this study we develop a generalizable analytical framework to maximise inferences from multi-pathogen serological studies. We fit the model to measurements of IgG antibody binding to 10 arboviral pathogens from a cross-sectional study in northwest Bangladesh with 1,453 participants. We used our framework to jointly infer the prevalence of each pathogen by location and age, as well as the levels of between-pathogen antibody cross-reactivity. We find evidence of endemic transmission of Japanese encephalitis virus as well as recent outbreaks of dengue and chikungunya viruses in this district. Our estimates of antibody cross-reactivity were highly consistent with phylogenetic distances inferred from genetic data. Further, we demonstrated how our framework can be used to identify the presence of circulating cross-reactive pathogens that were not directly tested for, representing a potential opportunity for the detection of novel emerging pathogens. The presented analytical framework will be applicable to the growing number of multi-pathogen studies and will help support the integration of serological testing into disease surveillance platforms.