While prime editing enables precise sequence changes in DNA, cellular determinants of prime editing remain poorly understood. Using pooled CRISPRi screens, we discovered that DNA mismatch repair (MMR) impedes prime editing and promotes undesired indel byproducts. We developed PE4 and PE5 prime editing systems in which transient expression of an engineered MMR-inhibiting protein enhances the efficiency of substitution, small insertion, and small deletion prime edits by an average 7.7-fold and 2.0-fold compared to PE2 and PE3 systems, respectively, while improving edit/indel ratios by 3.4-fold in MMR-proficient cell types. Strategic installation of silent mutations near the intended edit can enhance prime editing outcomes by evading MMR. Prime editor protein optimization resulted in a PEmax architecture that enhances editing efficacy by 2.8-fold on average in HeLa cells. These findings enrich our understanding of prime editing and establish prime editing systems that show substantial improvement across 191 edits in seven mammalian cell types.