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We present SHEEP, a new machine learning approach to the classic problem of astronomical source classification, which combines the outputs from the XGBoost, LightGBM, and CatBoost learning algorithms to create stronger classifiers. A novel step in our pipeline is that prior to performing the classification, SHEEP first estimates photometric redshifts, which are then placed into the data set as an additional feature for classification model training; this results in significant improvements in the subsequent classification performance. SHEEP contains two distinct classification methodologies: (i) Multi-class and (ii) one versus all with correction by a meta-learner. We demonstrate the performance of SHEEP for the classification of stars, galaxies, and quasars using a data set composed of SDSS and WISE photometry of 3.5 million astronomical sources. The resulting F1-scores are as follows: 0.992 for galaxies; 0.967 for quasars; and 0.985 for stars. In terms of the F1-scores for the three classes, SHEEP is found to outperform a recent RandomForest-based classification approach using an essentially identical data set. Our methodology also facilitates model and data set explainability via feature importances; it also allows the selection of sources whose uncertain classifications may make them interesting sources for follow-up observations.