Necessary Connections

Assume x and y are two non-overlapping (have no parts in common) contingent existents. It is then very plausible that there should be no necessary connections between them. That is, it should be possible for them to fail to co-exist as well as to co-exist. At least this is a fairly common assumption in the relevant literature.

It is further often assumed that two non-overlapping contingent existents should not be necessarily connected in virtue of some accidental intrinsic property they share.

I ask: how far should we push the spirit of such a denial of necessary connections? Is it plausible to hold that sometimes there should be no necessary connections between overlapping existents?

Take for example some plurality xx and its fusion ƒ(xx) (assuming it has one). Assume further that fusion is not a generalized form of identity (we all know what that means). Should we then hold that it is possible for xx to exist without ƒ(xx)? I think so. After all, they are not the same thing(s). Though it seems less plausible to hold that ƒ(xx) can exist without xx (though it is trickier than it might at first seem; cf. mereological essentialism). Do we here have a one-way necessary connection? Or, should we in general deny any necessary connection between any two things that are not identical (rather than non-overlapping)?

-Einar

PS: Personally, I think overlap is partial identity and that fusion is a form of identity, but most people don't for some reason. And that is why the above remarks are interesting.