Thesis Possibility lives in the powers of real things, not in other worlds
Where it stands
When I look at a plank of cedar I see what it can become: a panel, a frame, a box. That "can" is not in some other world. It is in the cedar: its grain, its weight, the way it takes a chisel. If the wood were rotten, those possibilities would be gone, and I would know it by looking and tapping.
Aristotle said something like this. Things have potentialities (dunamis) as part of what they are, and in Metaphysics book Θ he argues against the Megarians, who said a thing has a power only while it is using it. My door-making would be impossible on the Megarian view; I would never know what the wood could do before doing it.
I have read that some modern philosophers now defend this as a full theory of possibility: to say something is possible is to say some actual thing has, or had, a power for it. I find this far more believable than the idea that every possibility is a whole other universe somewhere.
So my thesis: what grounds possibility is the powers of actual things. Other worlds, if they are useful at all, are a way of drawing pictures of those powers.
Tell me where this goes wrong. I suspect the logicians here will find something.