With the growing global mental health crisis affecting over 970 million people, early identification of severity levels of stress, anxiety, and depression among students is important, as academic pressure and social transitions significantly affect their academic performance, personal development, and overall well-being. This study proposes a mathematical stacking ensemble model that integrates eight machine learning models Logistic Regression, Support Vector Machine, XGBoost, Gradient Boosting, Decision Tree, Artificial Neural Network, CatBoost, and Random Forest as meta learner for the prediction of severity levels of multiple mental disorders, such as stress, anxiety, and depression, among students at higher education institutions using a dataset of 2029 student records containing 68 psychological assessment scores, demographic, and academic factors. The methodology proceeds in four steps: data description and preprocessing, model development, mathematical formulation of the stacking ensemble model, and comparative analysis using evaluation metrics. The results reveal that the stacking ensemble model, validated through nested cross-validation, demonstrates high accuracies of 96% for stress, 98% for anxiety, and 99% for depression severities, outperforming individual models. These results confirm the effectiveness of the model, providing a reliable and scalable tool for predicting mental health risk detection in academic and clinical settings.