Abstract Designing optimized proteins is important for a range of practical applications. Protein design is a rapidly developing field that would benefit from approaches that enable many changes in the amino acid primary sequence, rather than a small number of mutations, while maintaining structure and enhancing function. Homologous protein sequences contain extensive information about various protein properties and activities that have emerged over billions of years of evolution. Evolutionary models of sequence co-variation, derived from a set of homologous sequences, have proven effective in a range of applications including structure determination and mutation effect prediction. In this work we apply one of these models (EVcouplings) to computationally design highly divergent variants of the model protein TEM-1 β-lactamase, and characterize these designs experimentally using multiple biochemical and biophysical assays. Nearly all designed variants were functional, including one with 84 mutations from the nearest natural homolog. Surprisingly, all functional designs had large increases in thermostability and most had a broadening of available substrates. These property enhancements occurred while maintaining a nearly identical structure to the wild type enzyme. Collectively, this work demonstrates that evolutionary models of sequence co-variation (1) are able to capture complex epistatic interactions that successfully guide large sequence departures from natural contexts, and (2) can be applied to generate functional diversity useful for many applications in protein design.