Nested logit models have been presented as an alternative to multinomial logistic models for multiple-choice test items (Suh and Bolt in "Psychometrika" 75:454-473, 2010) and possess a mathematical structure that naturally lends itself to evaluating the incremental information provided by attending to distractor selection in scoring. One potential concern in attending to distractors is the possibility that distractor selection reflects a different trait/ability than that underlying the correct response. This paper illustrates a multidimensional extension of a nested logit item response model that can be used to evaluate such distinctions and also defines a new framework for incorporating collateral information from distractor selection when differences exist. The approach is demonstrated in application to questions faced by a university testing center over whether to incorporate distractor selection into the scoring of its multiple-choice tests. Several empirical examples are presented.