Recent work has shown that multidimensionally scoring responses from different tests can provide better ability estimates. For educational assessment data, applications of this approach have been limited to binary scores. Of the different variants, the de la Torre and Patz model is considered more general because implementing the scoring procedure does not require prior knowledge of the correlational structure of the abilities, and existing item parameter estimates from traditional item response theory models can be utilized. This article extends the application of this method to data scored on ordered polytomous scales. A simulation study systematically examines how improvement in ability estimates is affected by factors such as the number of score categories, number of tests, test length, and correlation between abilities. Application of the method is illustrated using real data. Estimates of the abilities and the correlational structure are obtained using the Markov chain Monte Carlo method. (Contains 1 figure and 8 tables.)