Multiple imputation (MI) is one of the most popular methods for handling missing data in psychological research. However, many imputation approaches are poorly equipped to handle large numbers of variables, which are a common sight in studies that employ questionnaires to assess psychological constructs. In such a case, conventional imputation approaches often become unstable and require that the imputation model be simplified, for example, by removing variables or combining them into composite scores. In this article, we propose an alternative method that extends the fully conditional specification (FCS) approach to MI with dimension reduction techniques such as partial least squares (PLS). To evaluate this approach, we conducted a series of simulation studies, in which we compared it with other approaches that were based on variable selection, composite scores, or dimension reduction through principal components analysis (PCA). Our findings indicate that this novel approach can provide accurate results even in challenging scenarios, where other approaches fail to do so. Finally, we also illustrate the use of this method in real data and discuss the implications of our findings for practice.