Philosophers usually define nomological possibility in relative terms, as being compossible with the laws of nature. But this is inadequate, for it trivializes the nomological necessity of the natural laws themselves (as Kit Fine notes in 'The Varieties of Necessity').
Note that for any restrictive framework R, we can generically define R-possibility as follows: X is R-possible iff X is compossible with R. But not all such restrictions come with the same modal force. Consider R = 'grass is green'. This would not produce a fundamental partition of modal space. This particular choice of R lacks modal significance. Whether X is 'necessary' or 'possible' relative to grass being green, is not fundamental modal property of X. And although R itself is "R-necessary", this trivial fact does nothing to show that R is necessary in any fundamental or interesting sense, as the example of 'grass is green' shows.
The laws of nature seem importantly different in this respect. They have modal significance. There's a fundamental sense in which the laws of nature are necessary (despite being metaphysically contingent), which isn't captured by the triviality of saying that they're necessary relative to themselves. They seem to constitute a fundamental modal barrier, which cannot be passed without ascending to a higher order of possibility (e.g. metaphysical possibility).
It's easy enough to construct a space of scenarios or "possibilities". The crucial question is which divisions carve modal space at the joints. Put another way: what are the fundamental modal spaces? What are the ones which have genuine modal properties? And what do we even mean when we talk about this stuff? (The intuitive distinction seems clear enough. What's difficult is to see what the distinction consists in.)
Here's an idea: if we consider the broadest space of possible worlds, arranged according to similarity relations (so that "close possible worlds" are very similar to each other), perhaps we will find that there are some naturally occuring 'voids' in this space, separating 'galaxies' or clusters of possibilities. This would provide a principled basis for distinguishing varieties of possibility. Perhaps each galaxy corresponds to a set of natural laws. The void between them represents the fundamental modal 'barrier', the fact that it takes more "oomph" to overcome these restrictions than most.
To explicate this metaphorical talk: we require there to be certain patterns in the similarity relations that hold between possible worlds. In particular, there needs to be a significant dissimilarity between any pair of nomologically incompatible worlds.
But this notion of 'similarity' still seems awfully vague. How much this matters may depend on how much work we require the notion to do -- and this in turn depends on the order of explanation: are the worlds dissimilar because natural laws have brute modal significance, or do natural laws have modal significance because the relevant worlds exhibit brute dissimilarities?
The former sounds more promising to me. But whichever way it goes, we must appeal to some form of primitive ("brute") modal properties at some point. And that raises all kinds of problems. (What are these properties? How do we grasp them?)
P.S. I wonder what other contenders for "fundamentally significant modal spaces" we can identify? Perhaps historical possibility, where that's understood to require compossibility with both the natural laws and the "initial conditions" of the universe. Or dynamic possibility, which requires compossibility with the natural laws and the current state of affairs. And of course my notion of real possibility (positive or negative?), if it's coherent. Any other suggestions?