Bayesian Model Averaging (BMA) has recently been proposed as a method for statistical postprocessing of forecast ensembles from numerical weather prediction models. The BMA predictive probability density function (PDF) of any weather quantity of interest is a weighted average of PDFs centered on the bias-corrected forecasts from a set of different models. However, current applications of BMA calibrate the forecast specific PDFs by optimizing a single measure of predictive skill. Here we propose a multi-criteria formulation for postprocessing of forecast ensembles. Our multi-criteria framework implements different diagnostic measures to reflect different but complementary metrics of forecast skill, and uses a numerical algorithm to solve for the Pareto set of parameters that have consistently good performance across multiple performance metrics. Two illustrative case studies using 48-hour ensemble data of surface temperature and sea level pressure, and multi-model seasonal forecasts of temperature, show that a multi-criteria formulation provides a more appealing basis for selecting the appropriate BMA model.