Group testing is a widely used binary classification method that efficiently distinguishes between samples with and without a binary-classifiable attribute by pooling and testing subsets of a group. Bayesian Group Testing (BGT) is the state-of-the-art approach, which integrates prior risk information into a Bayesian framework to minimize tests and reduce false classifications. However, BGT struggles with multinomial group testing, where samples have multiple binary-classifiable attributes that must be distinguished simultaneously. We address this need by proposing Bayesian Multinomial Group Testing (BMGT), which includes a new Bayesian-based model and supporting theorems for efficient and precise multinomial group testing. We further design and develop SBMGT, a high-performance and scalable framework to tackle BMGT’s computational challenges by proposing three key innovations: 1) a parallel binary-encoded product lattice model with up to 99.8% efficiency; 2) the Bayesian Balanced Partitioning Algorithm (BBPA), a multinomial pooling strategy optimized for parallel computation with up to 97.7% scaling efficiency on 4096 cores; and 3) a scalable multinomial group testing analytics framework, demonstrated in a real-world disease surveillance case study using AIDS and STDs datasets from Uganda, where SBMGT reduced tests by up to 54% and lowered false classification rates by 92% compared to BGT.