The single-strategy deterministic, inputs, noisy "and" gate (SS-DINA) model has previously been extended to a model called the multiple-strategy deterministic, inputs, noisy "and" gate (MS-DINA) model to address more complex situations where examinees can use multiple problem-solving strategies during the test. The main purpose of this article is to adapt an efficient estimation algorithm, the Expectation–Maximization algorithm, that can be used to fit the MS-DINA model when the joint attribute distribution is most general (i.e., saturated). The article also examines through a simulation study the impact of sample size and test length on the fit of the SS-DINA and MS-DINA models, and the implications of misfit on item parameter recovery and attribute classification accuracy. In addition, an analysis of fraction subtraction data is presented to illustrate the use of the algorithm with real data. Finally, the article concludes by discussing several important issues associated with multiple-strategies models for cognitive diagnosis.