Personally I also require those groups to include at least one special character.

Your schema doesn’t account for companies that only have a management tack or an ic track with no opportunity for someone to sometimes lead teams and sometimes make technical decisions. I think you’ll find it’s better if you simply encompass the natural numbers.

According to Gödel's incompleteness theorems, there never exists a complete set of types of people, because there’s always one more type — people writing about those types.