Multistage testing (MST), a variant of computerized adaptive testing (CAT), differs from conventional CAT in that it is adapted at the module level rather than at the individual item level. Typically, all examinees begin the MST with a linear test form in the first stage, commonly known as the routing stage. In 2020, Han introduced an innovative concept known as Intersectional Routing (ISR), which allows module selection in the first stage of the MST based on the examinees' estimated scores. These scores were predicted using a variety of information, including background data and other correlated latent traits. In this study, we extend Han's ISR framework to a multidimensional test comprising multiple unidimensional subtests. In a multidimensional test, the correlation coefficients between the latent traits can be estimated by fitting a multidimensional item response theory model. Our extension allows module selection in the first stage of each subtest to consider information from all the other subtests via the known correlation matrix. The results of simulation studies showed that our extension improved the measurement compared with typical MST designs in conditions with moderate intercorrelations across module designs. The practical insights were given in the empirical analysis.