Multi-principal element alloys (MPEAs) have recently garnered considerable attention due to their unique microstructural characteristics. These alloys have superior corrosion resistance and mechanical properties achievable through their complex compositions. In this study, based on two data sets, various machine learning (ML) methods were used to predict phases of MPEAs using statistical measures and the interactions of the features. The critical features, namely valence electron concentration, mixing enthalpy, mixing entropy, melting temperature, and electronegativity, demonstrated utmost significance, yielding phase detection accuracies within 68.0% to 97.7%. Subsequently, we devised a two-layered Bayesian shrinkage method for predicting mechanical properties, including microhardness, ultimate and yield strength, elastic modulus, and elongation. This approach stacked the prediction power and model-based clustering of Support Vector Machine Regression (SVMreg), Random Forest Regression (RFreg), and a Mixture of Linear Regression with Experts. The Bayesian method we proposed surpasses the performance of conventional ML methods in predicting the mechanical properties of MPEAs. We then validated the models using experimental assessments.