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When nature evolves a gene over eons at scale, it produces a diversity of homologous sequences with patterns of conservation and change that contain rich structural, functional, and historical information about the gene. However, natural gene diversity accumulates slowly and likely excludes large regions of functional sequence space, limiting the information that is encoded and extractable. We introduce upgraded orthogonal DNA replication (OrthoRep) systems that radically accelerate the evolution of chosen genes under selection in yeast. When applied to a maladapted biosynthetic enzyme, we obtained collections of extensively diverged sequences with patterns that revealed structural and environmental constraints shaping the enzyme's activity. Our upgraded OrthoRep systems should support the discovery of factors influencing gene evolution, uncover previously unknown regions of fitness landscapes, and find broad applications in biomolecular engineering.