If essence is analyzed via Kit Fine's own modal primitivism, the necessity of membership in singleton sets can be blocked by restricting the relevant modal base to natural-kind worlds, preserving intensionality.
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Singleton sets(as the mathematical objects whose membership is being discussed)
In mathematics and logic, a set that contains only one thing—like a box with a single item inside it.
essence(Medieval realist metaphysics)
The defining nature of a species, held by some to be distinct from and capable of surviving the destruction of all individual members of that species
intensionality(Used to characterize attitudinal sentences, predicate modifiers, and non-extensional contexts)
The property of a sentence or expression whose meaning (and truth value) depends on the meaning (intension) of its constituent expressions, not merely their truth value or extension
modal base(Kratzer's modal semantics for ability ascriptions)
A contextually-specified set of facts that determines which possible worlds are accessible for evaluating an ability ascription