(1) Background: Machine learning (ML) methods are rarely used for an omics-based prescription of cancer drugs, due to shortage of case histories with clinical outcome supplemented by high-throughput molecular data. This causes overtraining and high vulnerability of most ML methods. Recently, we proposed a hybrid global-local approach to ML termed floating window projective separator (FloWPS) that avoids extrapolation in the feature space. Its core property is data trimming, i.e., sample-specific removal of irrelevant features. (2) Methods: Here, we applied FloWPS to seven popular ML methods, including linear SVM, nearest neighbors (kNN), random forest (RF), Tikhonov (ridge) regression (RR), binomial naïve Bayes (BNB), adaptive boosting (ADA) and multi-layer perceptron (MLP). (3) Results: We performed computational experiments for 21 high throughput gene expression datasets (41-235 samples per dataset) totally representing 1778 cancer patients with known responses on chemotherapy treatments. FloWPS essentially improved the classifier quality for all global ML methods (SVM, RF, BNB, ADA, MLP), where the area under the receiver-operator curve (ROC AUC) for the treatment response classifiers increased from 0.61-0.88 range to 0.70-0.94. We tested FloWPS-empowered methods for overtraining by interrogating the importance of different features for different ML methods in the same model datasets. (4) Conclusions: We showed that FloWPS increases the correlation of feature importance between the different ML methods, which indicates its robustness to overtraining. For all the datasets tested, the best performance of FloWPS data trimming was observed for the BNB method, which can be valuable for further building of ML classifiers in personalized oncology.