Neuropsychiatric disorders often involve dysregulation of serotonergic and dopaminergic pathways. This study applied machine learning (ML) with quantitative structure-activity relationship (QSAR) methods to predict the bioactivity (-log half-maximal inhibitory concentration (pIC50)) of compounds targeting both receptor families, aiming to identify multitarget inhibitors among US Food and Drug Administration (FDA)-approved drugs. A dataset of 5,628 compounds with experimental IC50 values was obtained from ChEMBL and encoded with PubChem fingerprints. Random Forest and Extreme Gradient Boosting models were trained, optimized, and evaluated with 5-fold cross-validation, and Shapley Additive Explanations (SHAP) values were used for interpretation. After outlier removal and descriptor selection, models achieved coefficient of determination (R2) test ca. 0.69 and were used to screen over 1,500 approved drugs. A total of 162 were predicted to have dual bioactivity (pIC50 > 6, coefficient of variation < 1%), including antipsychotics, adrenergic agonists (e.g., epinephrine), dopamine agonists (e.g., levodopa), antihistamines (e.g., cyproheptadine), antiemetics (e.g., droperidol), ergot alkaloids (e.g., ergotamine), antibiotics (e.g., penicillin G), and lipid-lowering agents (e.g., pravastatin). Key molecular descriptors indicated the relevance of nitrogen-containing fragments and conjugated aromatic substructures for dual receptor binding. These results provide a computational framework for repurposing drugs and guiding experimental validation in neuropsychiatric research.