Is it possible that there are no three-way interactions in a multiple regression model that includes four predictors?

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Yes, it is possible that there are no three-way interactions in a multiple regression model that includes four predictors. A three-way interaction involves the combined effect of three predictors on the outcome variable, while a multiple regression model with four predictors could have two-way interactions, main effects, or no interactions at all. The absence of a three-way interaction does not necessarily imply that the predictors do not interact with each other or explain a significant amount of variance in the outcome variable, but this would need to be examined through other types of analyses or diagnostic tests.