This is an outline with proofs omitted. Start with a notion of necessity L that satisfies the constraints of System T and take as an axiom the Natural Numbers Barcan Formula (NNBF):
- L(n)(Fn) iff (n)LFn,
Now, we can bootstrap our way up to a logic satisfying S4 from the logic that uses L. Let Lnp be L...Lp with n Ls. Let L*p be (n)Lnp. I think the following is true, though it may take some work to prove it and will need for every p a predicate F such that Fn iff Lnp: if L satisfies System T and NNBF is an axiom, then L* satisfies S4. Moreover, intuitively, L* has every bit as much, and maybe more, right to be called "metaphysical necessity" as L does. So, given a modal logic that satisfies T and NNBF, both of which are pretty plausible, we can define a metaphysical necessity operator that satisfies S4. I think this makes it plausible that ordinary metaphsyical necessity satisfies S4.