Alignments of orthologous protein sequences convey a complex picture. Some positions are utterly conserved whilst others have diverged to variable degrees. Amongst the latter, many are non-exchangeable between extant sequences. How do functionally critical and highly conserved residues diverge? Why and how did these exchanges become incompatible within contemporary sequences? Our model is phosphoglycerate kinase (PGK), where lysine 219 is an essential active-site residue completely conserved throughout Eukaryota and Bacteria, and serine is found only in archaeal PGKs. Contemporary sequences tested exhibited complete loss of function upon exchanges at 219. However, a directed evolution experiment revealed that two mutations were sufficient for human PGK to become functional with serine at position 219. These two mutations made position 219 permissive not only for serine and lysine, but also to a range of other amino acids seen in archaeal PGKs. The identified trajectories that enabled exchanges at 219 show marked sign epistasis - a relatively small loss of function with respect to one amino acid (lysine) versus a large gain with another (serine, and other amino acids). Our findings support the view that, as theoretically described, the trajectories underlining the divergence of critical positions are dominated by sign epistatic interactions. Such trajectories are an outcome of rare mutational combinations. Nonetheless, as suggested by the laboratory enabled K219S exchange, given enough time and variability in selection levels, even utterly conserved and functionally essential residues may change.