Is the Possible Necessarily General?

I'm not going to try to settle this question right now, but merely to point out some of the consequences of answering it with either a 'yes' or a 'no'.

Charles Peirce once said "The possible is necessarily general; and no amount of general specification can reduce a general class of possibilities to an individual case." (Collected Papers 4.172). If this is right, then it seems to me that certain consequences follow:

(1) Merely possible worlds contain no individuals. Hence, no individual (not even God) exists in all possible worlds or in any world but the actual one.
(2) The coming into being of the actual world is not simply the instantiation of a possible world but its individuation.
(3) Divine providence of necessity must be general, not meticulous. That rules out Molinism and Augustinianism, but leaves room for either process theism or versions of open theism that limit omniscience.

In contrast to Peirce, I am inclined to hold that possible worlds are just as individuated as the actual world. If this is right, then,

(1') Merely possible worlds do contain individuals. Hence, it is possible that some individuals exist in multiple worlds.
(2') The coming into being of the actual world just is the instantiation of a possible world.
(3') Divine providence need not be general, but may (though I think need not) be meticulous. All of the competing providential options are still on the table (at least as far as this issue goes).

I should note that, in contrast to possibilists like David Lewis, I do not think that all possible worlds are ontologically on par with each other. There is one, the actual world, that uniquely obtains. All others "exist" in some abstract sense, perhaps in the mind of God.