David Lewis's counterpart theory can explain the asymmetry between 'essentially human' and 'essentially human and a set-member' via differences in counterpart relations across contexts, without invoking hyperintensionality.

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Contexts(as what gets fed into Kaplan's character function): The specific circumstances in which something is said—things like who is speaking, where they are, and when they're speaking.
Counterpart relations(different rules for matching objects across possible worlds): The different ways we can decide which alternate-world versions of something 'count as' the same thing for purposes of understanding what could be true about it.
Counterpart theory(as used in metaphysics and modal logic): A way of thinking about possible worlds where instead of asking 'could I have been different?', you ask 'is there a version of me in another possible world that is different?' That other version is your 'counterpart.'
David Lewis(the philosopher who created this theory): An influential American philosopher (1941-2001) who developed Counterpart Theory as a way to understand how we talk about objects in different possible worlds.

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