Durston's FI

Myosins are a perfect example of such a family:
https://www.researchgate.net/figure/Different-classes-of-myosin-superfamily-Phylogenetic-tree-of-114-myosin-sequences_fig7_221686367

There is a good test case for #2 in this family, as there are many clinical papers documenting mutations in the beta-cardiac myosin heavy chain (MYH7) gene, nearly all of which are likely to be functional, large numbers of which have been assayed for enzymatic activity, and only rarely cause disease (epistasis is the likely reason).