If the entailment chain through intermediate supervenience presupposes a fixed domain of individuals across worlds, it fails in variable-domain modal frameworks standard in philosophical logic.

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Fixed domain(as used in logic): A set of things (like people, objects, or properties) that stays exactly the same and doesn't change.
Modal frameworks(as used in logic): Systems of logic that deal with possibility, necessity, and related concepts—thinking about what must be true, what could be true, or what's impossible.
Philosophical logic(as the field analyzing the concepts in this statement): The study of reasoning and arguments using precise logical systems, focusing on what makes arguments valid and how language works in reasoning.
Variable-domain(as used in logic): A framework where the collection of things that exist can differ between different scenarios or possible worlds.
entailment(Conceptualist framework): Understood in terms of truth at a world
possible worlds(Leibniz's modal semantics, anticipating contemporary possible-worlds semantics): Worlds that have existence in a tenuous sense; fictional worlds used to characterize the nature of possibles that are never actualized
supervenience(Philosophy of mind and reduction; contrasted with full reduction): A relation in which mental (or higher-level) states are dependent on physiological (or lower-level) states such that any two cases with identical lower-level bases are identical in their higher-level states; a necessary but not sufficient condition for reduction.

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