Inspired by the extensive hierarchies present in complexity theory, I wondered if such hierarchies were also present for type systems. However, the two examples I've found so far are both more like checklists (with orthogonal features) rather than hierarchies (with successively more and more expressive type systems).
The two examples I have found are the Lambda cube and the concept of k-ranked polymorphism. The first one is a checklist with three options, the second is a real hierarchy (though k-ranked for specific values of k is uncommon I believe). All other type system features I know of are mostly orthogonal.
I'm interested in these concepts because I'm designing my own language and I'm very curious how it ranks among the currently existing type systems (my type system is somewhat unconventional, as far as I know).
I realise that the concept of 'expressiveness' might be a bit vague, which may explain why type systems seem like checklists to me.