The usefulness of the general Rasch model for multidimensional data, from the most simple formulations to the more complex versions of the model, is explored. Also investigated was whether the parameters of the models could be readily interpreted. Models investigated included: (1) the vector model; (2) the product term model; (3) the vector and product term model; (4) the reduced vector and product term model; and, (5) the item cluster model. Of the models investigated, all but the reduced vector and product term model and the item cluster model were rejected as incapable of reasonably modelling realistic multidimensional data. The item cluster model appears to be a useful model, but its applications may be limited in scope. The reduced vector and product term model was found to be the most capable of modelling realistic multidimensional data. Although the estimation of the parameters of the reduced vector and product term model may be more difficult than it would be for other models, this model appears to be the model that is most worth pursuing. (Author/PN)