In S4 or S5, or a derivative therefrom, can an individual exist in every possible world without contradiction? — Banno

I don't think you even need S5 for it? Given that you can choose world elements.

W1={egg, bacon}

W2={egg}

The statement E: "At least one entity in this world is an egg"

E's w1 valuation, true.
E's w2 valuation, true.
E is true in all possible worlds, so it's necessary.

If you'd like, call the relation between W1 and W2 the breakfastibility relation. Two worlds are connected iff they consist of only breakfast goods. That accessibility relation is an equivalence relation on the set of possible worlds.

So yes, with that world set and that accessibility relation, I believe the existence of eggs is necessary.

#modal logic isn't metaphysics