I have the legal right as a person to write on a piece of paper "i am a person". That piece of paper does not inherit any rights by my doing so.
Me writing "Microsoft" on one paper and "Google" on another paper certainly means that those two pieces of paper are distinct. Neither one, however, has rights.
What I meant by intermingling/combination/whatever is that, there are no rights to inherit, because a piece of paper has no rights, inherited or otherwise. That includes intermingled rights of people. People may have complex intermingled rights on certain subjects. That is not applicable to legal fictions, because they don't have rights and can't inherit rights.
I think it will become clear as you picture the silly idea of writing "I'm a piece of paper and I have rights" and then expecting that to mean anything. Work backwards from there.