Polytomous attributes, particularly those defined as part of the test development process, can provide additional diagnostic information. The present research proposes the polytomous generalized deterministic inputs, noisy, "and" gate (pG-DINA) model to accommodate such attributes. The pG-DINA model allows input from substantive experts to specify attribute levels and is a general model that subsumes various reduced models. In addition to model formulation, the authors evaluate the viability of the proposed model by examining how well the model parameters can be estimated under various conditions, and compare its classification accuracy against that of the conventional G-DINA model with a modified classification rule. A real-data example is used to illustrate the application of the model in practice.