When the highest-way association is present in a 3-way cross-classification of frequencies, standard logit and loglinear models have an many parameters as there are cells in the table; that is, the models are "saturated." Extensions of logit and loglinear models are described here that provide more parsimonious alternatives to saturated models. The new models, logit multiplicative models, and their equivalent log multiplicative models, are introduced here for the case where there is one dichotomous response or criterion variable and two (polytomous) explanatory or predictor variables. In logit multiplicative models, the interaction between the explanatory variables is represented by the product of scale values for the categories of the explanatory variables and a measure of the strength of the association. Plots of the scale values provide graphical representations and descriptions of the interaction. The new models are illustrated by modeling a 3-way interaction between whether an elementary school student attends an extracurricular tutoring program, the highest educational level attained by the student's father, and the student's grade level. (Contains 1 figure, 3 tables, and 33 references.) (Author)