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The predictive performance of polygenic scores (PGS) is largely dependent on the number of samples available to train the PGS. Increasing the sample size for a specific phenotype is expensive and takes time, but this sample size can be effectively increased by using genetically correlated phenotypes. We propose a framework to generate multi-PGS from thousands of publicly available genome-wide association studies (GWAS) with no need to individually select the most relevant ones. In this study, the multi-PGS framework increases prediction accuracy over single PGS for all included psychiatric disorders and other available outcomes, with prediction R increases of up to 9-fold for attention-deficit/hyperactivity disorder compared to a single PGS. We also generate multi-PGS for phenotypes without an existing GWAS and for case-case predictions. We benchmark the multi-PGS framework against other methods and highlight its potential application to new emerging biobanks.