Much of modern discussion of modality in philosophy is concerned with possible worlds analysis. A question that one has to ask, though, is how adequate it is to talking about all matters of modality. An advantage of possible worlds semantics is that it is very flexible. It sometimes takes contortions and ingenious somersaults, but you can use it to talk about a very wide variety of modalities -- alethic, deontic, doxastic, epistemic, temporal, locative, and so forth. So there's no question that you can cover a lot of ground. But is there anything that is dropping out? Suppose you have something that is not possible but superpossible, in the sense that it is something such that it makes perfect sense to think of it as possible but also such that it makes no sense to think of it as a possible world or as a collection of possible worlds or as an element in a single possible world. There are at least two obvious candidates for a superpossible in this sense.
(1) The Actual World. One of the longstanding problems with the 'possible worlds' vocabulary is that it makes people think it is talking about worlds. To be sure, you could be, but there's nothing about either the formal structure or the semantics that requires that we be literally talking about a world. Now, this would be at most a minor confusion most of the time, but I think in one case it regularly hangs people up, and that case is this: it's very tempting to think of the actual world as a possible world. I mean, it's almost irresistible to talk that way; if the world is actual, it is possible, and therefore it is a possible world. But as far as possible-worlds talk goes this is, first, not necessary, and, second, wrong. Possible worlds semantics, as such, of course, has no actuality; you can add an actuality operator to it, but that's an additional complication bringing in a number of questions, not all of which are easy to answer. But there is very good reason to say this: if there are possible worlds, none of them are the actual world. And this is because the only reason for talking about these 'possible worlds' is so that we may more easily work out issues concerned with actual possibilities. And the diverse actual possibilities are possibilities available to the actual world. That is to say: if we are to make any sense of possible worlds at all, it seems we have to take the whole manifold of possible worlds as a way of talking about the possibilities inherent in the actual world. If the actual world can be more than one way, no single 'possible world' can be an adequate representation of it. But the actual world is certainly possible. The actual world thus seems to be superpossible.
(2) God. If one talks about God as a necessary being, you can gloss that as "existing in all possible worlds". But is this adequate? There seems to be plenty of reason to think it couldn't be. It might be a true statement in the vocabulary of possible worlds; but the question is whether it captures what it is for God to be a necessary being. To see why it does not appear to do so, consider for a moment where we get all of this possible worlds talk from. People have always talked about modality; but talking about modality in terms that start to look like our possible worlds talk really begins in earnest with the Molinists. Their phrase was 'order of nature', and their reason for talking about them was that God has the power to create many different world-histories (so to speak), and so, they said, he could consider these different possible divine plans and what they would involve as part of His 'middle knowledge'. (It was 'middle' in the sense that it wasn't simply God knowing His own capabilities, and it wasn't simply God knowing what He willed to exist, but was in between, like deliberation is in between understanding what you can do and knowing that you've chosen this particular thing to do.) God would consider what 'order of nature' -- a whole world from beginning to ending -- that He would make to exist, and then, having chosen one, create it. These orders of nature cannot be capturing modalities concerned with God Himself, even though God does in some sense exist in the actual order of nature, because God is what makes the orders of nature (1) orders of nature and (2) things that can be actual in the first place. This is not exactly how modern notions of possible worlds work, but a similar sort of issue arises with respect to possible worlds as arises with their ancestors. To say that God exists in all possible worlds does not do justice to what is meant by saying that God's existence is necessary, because it doesn't capture the fact that God is not merely 'in all possible worlds' but in some sense has a priority to other possible things. 'Possible worlds', if they are to be of any value at all, can't just be loose bags of possible things; they have structure, and that structure means that some things in them depend on other things. When people talk about God as being necessary, God is not treated as just something that exists, nor even just something that exists no matter what. God shows up as world-actualizer, as actual-possibility-maker, as making it possible for everything else to be actual. God has a fundamentality with respect to other possibilities that is not at all captured by talking about being in all possible worlds. Thus God seems to be superpossible.
Both of these are, of course, connected, since if the actual world is superpossible, and if God is the reason for the actual world's being actual, God must be superpossible.
Whenever we are talking about modality and its relation to the actual world or to God, we run into regular interpretive issues; they both massively increase the complexity and ingenuity that has to be used in order to deploy possible worlds to analyze modal questions. They aren't necessarily useless, but they constantly lack something that is needed, and the wrong turns you can make -- leading you to some really weird conclusions -- multiplies. This is borne up by looking at how modalities are actually handled in dealing with the actual world or God. And I think the reason is that the actual world and God are in terms of modality so rich that they exceed the resources of possible world semantics to capture. You can still say useful things; but you can't say everything that needs to be said. And it becomes a question, of course, whether there are other superpossibles.