A multidimensional Rasch-type item response model, the multidimensional random coefficients multinomial logit model, is presented as an extension to the Adams and Wilson (1996) random coefficients multinomial logit model. The model is developed in a form that permits generalization to the multidimensional case of a wide class of Rasch models, including the simple logistic model, Masters' partial credit model, Wilson's ordered partition model, and Fischer's linear logistic model. Moreover, the model includes several existing multidimensional models as special cases, including Whitely's multicomponent latent trait model, Andersen's multidimensional Rasch model for repeated testing, and Embretson's multidimensional Rasch model for learning and change. Marginal maximum likelihood estimators for the model are derived and the estimation is examined using a simulation study. Implications and applications of the model are discussed and an example is given.