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Multi-study learning uses multiple training studies, separately trains classifiers on individual studies, and then forms ensembles with weights rewarding members with better cross-study prediction ability. This article considers novel weighting approaches for constructing tree-based ensemble learners in this setting. Using Random Forests as a single-study learner, we perform a comparison of either weighting each forest to form the ensemble, or extracting the individual trees trained by each Random Forest and weighting them directly. We consider weighting approaches that reward cross-study replicability within the training set. We find that incorporating multiple layers of ensembling in the training process increases the robustness of the resulting predictor. Furthermore, we explore the mechanisms by which the ensembling weights correspond to the internal structure of trees to shed light on the important features in determining the relationship between the Random Forests algorithm and the true outcome model. Finally, we apply our approach to genomic datasets and show that our method improves upon the basic multi-study learning paradigm.