“A friend of his” type expression for abstract entities

Question

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.

Answer 1

I would have cast that sentence as "What can we do with assignments and their heirarchies?". I can't even imagine saying, "I sat on the table, and a leg of its was wobbly." I can't think of an inanimate example were that construction sounds natural.