grammaticality - "A friend of his" type expression for abstract entities

Like many non-native speakers, formulations like "a friend of his" strike me as counter-intuitive, but I'm trying to adapt. Now I have a strange situation: I want to apply it to abstract entities. The sentence would be:

"What can we do with assignments and hierarchies of theirs?"

(I use assignments because I'm trying to avoid repetition. In the real text it's "blabla transmogrifying assignments").

I think this sounds awkward, and I can't recall ever having read anything like that. Is it possible that this type of construction is only valid for people? Or maybe it's a slightly different meaning of "of", and there's no possessive aspect to my usage of "of"?

I'm aware of Why do you say "friend of mine" instead of "friend of me"?
and
Is "a friend of his" a used phrase? but all the examples had a person as the possessing subject.