In addition to naturally occurring types of catalytic triads, protein engineering has been used to create enzyme variants with non-native amino acids, or entirely synthetic amino acids. Catalytic triads have also been inserted into otherwise non-catalytic proteins, or protein mimics.
Subtilisin (a serine protease) has had its  oxygen nucleophile replaced with each of sulfur, selenium, or tellurium. Cysteine and selenocysteine were inserted by mutagenesis, whereas the non-natural amino acid, tellurocysteine, was inserted using auxotrophic cells fed with synthetic tellurocysteine. These elements are all in the 16th periodic table column (chalcogens), so have similar properties. In each case, changing the nucleophile reduced the enzyme's protease activity, but increased a different activity. A sulfur nucleophile improved the enzymes transferase activity (sometimes called subtiligase). Selenium and tellurium nucleophiles converted the enzyme into an oxidoreductase. When the nucleophile of TEV protease was converted from cysteine to serine, it protease activity was strongly reduced, but was able to be restored by directed evolution.
Non-catalytic proteins have been used as scaffolds, having catalytic triads inserted into them which were then improved by directed evolution. The Ser-His-Asp triad has been inserted into an antibody, as well as a range of other proteins. Similarly, catalytic triad mimics have been created in small organic molecules like diaryl diselenide, and displayed on larger polymers like Merrifield resins, and self-assembling short peptide nanostructures.