IRT-based models with a general ability and several specific ability dimensions are useful. Studies have looked at item response models where the general and specific ability dimensions form a hierarchical structure. It is also possible that the general and specific abilities directly underlie all test items. A multidimensional IRT model with such an additive structure is proposed under the Bayesian framework. Simulation studies were conducted to evaluate parameter recovery as well as model comparisons. A real data example is also provided. The results suggest that the proposed additive model offers a better way to represent the test situations not realized in existing models.