The ability to deliver large transgenes to a single genomic sequence with high efficiency would accelerate biomedical interventions. Current methods suffer from low insertion efficiency and most rely on undesired double-strand DNA breaks. Serine integrases catalyze the insertion of large DNA cargos at attachment (att) sites. By targeting att sites to the genome using technologies such as prime editing, integrases can target safe loci while avoiding double-strand breaks. We developed a method of phage-assisted continuous evolution we call IntePACE, that we used to rapidly perform hundreds of rounds of mutagenesis to systematically improve activity of PhiC31 and Bxb1 serine integrases. Novel hyperactive mutants were generated by combining synergistic mutations resulting in integration of a multi-gene cargo at rates as high as 80% of target chromosomes. Hyperactive integrases inserted a 15.7 kb therapeutic DNA cargo containing von Willebrand Factor. This technology could accelerate gene delivery therapeutics and our directed evolution strategy can easily be adapted to improve novel integrases from nature.