The rapid and escalating spread of SARS coronavirus 2 (SARS-CoV-2) poses an immediate public health emergency. The viral spike protein S binds ACE2 on host cells to initiate molecular events that release the viral genome intracellularly. Soluble ACE2 inhibits entry of both SARS and SARS-2 coronaviruses by acting as a decoy for S binding sites, and is a candidate for therapeutic, prophylactic and diagnostic development. Using deep mutagenesis, variants of ACE2 are identified with increased binding to the receptor binding domain of S. Mutations are found across the interface, in the N90-glycosylation motif, and at buried sites where they are predicted to enhance local folding and presentation of the interaction epitope. When single substitutions are combined, large increases in binding can be achieved. The mutational landscape offers a blueprint for engineering high affinity proteins and peptides that block receptor binding sites on S to meet this unprecedented challenge.