A primary goal of polygenic scores, which aggregate the effects of thousands of trait-associated DNA variants discovered in genome-wide association studies (GWASs), is to estimate individual-specific genetic propensities and predict outcomes. This is typically achieved using a single polygenic score, but here we use a multi-polygenic score (MPS) approach to increase predictive power by exploiting the joint power of multiple discovery GWASs, without assumptions about the relationships among predictors. We used summary statistics of 81 well-powered GWASs of cognitive, medical and anthropometric traits to predict three core developmental outcomes in our independent target sample: educational achievement, body mass index (BMI) and general cognitive ability. We used regularized regression with repeated cross-validation to select from and estimate contributions of 81 polygenic scores in a UK representative sample of 6710 unrelated adolescents. The MPS approach predicted 10.9% variance in educational achievement, 4.8% in general cognitive ability and 5.4% in BMI in an independent test set, predicting 1.1%, 1.1%, and 1.6% more variance than the best single-score predictions. As other relevant GWA analyses are reported, they can be incorporated in MPS models to maximize phenotype prediction. The MPS approach should be useful in research with modest sample sizes to investigate developmental, multivariate and gene-environment interplay issues and, eventually, in clinical settings to predict and prevent problems using personalized interventions.