So, I'm trying to make sense of the notion of 'possibility'. Again. I think it might be worth distinguishing the fundamental modal concept from various quasi-modal pretenders. By the latter, I have in mind the 'relative' and merely formal notion of what is 'allowed' within some limiting framework. We might, for example, define the 'logically possible' as that which entails no contradictions. (There it seems the fundamental notion - "contradiction" - is logical, not modal.) More generally, for any framework of limitations F, something is F-possible iff it is allowed by the rules of F. (I assume [perhaps falsely?] that this notion of what's "allowed" can be spelled out in non-modal terms.) But such relational accounts fail to do justice to our absolute concept. For any claim of "F-possibility", we can ask: "Yes, but is it really possible?"
The fundamental modal concept, then, concerns what really could have been the case. This seems conceptually distinct from logical notions of consistency and such. It's difficult to get a grip on, but I think we can roughly illustrate the concept by imagining time "rewinding", and then replaying with a different outcome. That alternative outcome is seen to be a "real possibility", or a way the world really could have turned out. The notion is clearer with regard to the future: we might think that the future is 'open' in various ways, that any one of various alternatives really could eventuate. Extending this intuitive notion back into the past, we will find various (now closed) branches that really were, at one point, metaphysically open possibilities.
The problem with this picture is that, at best, it only gets us as far as nomological possibility (worse, nomological possibility given initial starting conditions). But our intuitive notion of metaphysical possibility needs to be broader than that. It seems plausible that there really could have been different laws of nature, or different 'starting conditions', right back at [before?] the very beginning of time. (Perhaps there could have been no time at all!) But I'm not sure how to make sense of alternate possibilities atemporally.
We might imagine God choosing what physical laws (etc.) to make, or what possible world to actualize. Then the metaphysically ("really") possible worlds are those that God really might have chosen to make. Intuitively, a world W is metaphysically possible iff were we to 'rewind and replay' the decision enough times, then God would eventually actualize W.
Of course, that's a terribly rough notion. It wouldn't do as an analysis, since it appeals to modal (at least, counterfactual) notions itself. And it isn't clear whether the intuitive idea of "rewinding" God's atemporal decisions is genuinely coherent. (It isn't even clear whether the notion of an "atemporal decision" is coherent.) Also, I don't think God exists, which of course poses problems for any attempt to take this heuristic too literally! But I don't think God is playing any crucial role here (other than making the illustration a little easier to follow); we might just as well consider any other atemporal indeterminacy, or way in which it could somehow be "metaphysically open" which world gets to be made actual. (Atemporal indeterminacy really is a bizarre notion. Has anyone written about such things before? Sounds like the kind of thing theologians should be concerned about, at least. But of course I'd be more interested in analytic metaphysicians.)
So: while I'd previously given up on the concept of 'real possibility', I hope the above illustrations help to indicate that there is a rough concept in this vicinity. I'm not sure whether it can withstand further analysis though. (It does seem a very confused notion. Or, at least, I am very confused by it!) And it might be that the standard quasi-modal notions are all we really need for our philosophical purposes. (Perhaps my characterization of them is unfair, and they are fundamentally modal, but in a slightly difference sense to what I tried to point to above. I guess a lot hinges on the analysis of 'allowance' hinted at above.)
Fun but confusing topic. Comments welcome (as always).
P.S. Though the concept is distinct, absolute possibility will presumably end up coinciding with some limiting framework or other. For example, it may be that the world could really have turned out in any logically possible way. I take this to be a substantive claim, however, so the concepts of 'logically possible' and 'way the world really could have been' should be kept distinct.