Contingent Examples of Term-Relative Intrinsicality?

Zylstra's work shows that, if we are going to try to analyze essence in terms of necessity and intrinsicality and deliver the goods on Fine's celebrated Socrates/{Socrates} example (Socrates does not belong essentially to {Socrates}, but {Socrates} essentially contains Socrates), we had better understand intrinsicality as term-relative, at least in the case of relations. That is, we can't just say that some relations are intrinsic and others are extrinsic and that's it - rather, some two-place relations are, so to speak, intrinsic on one side but extrinsic on the other.

But can we really explicate such a concept of intrinsicality? Or is this really just going to be the concept of essence which we end up explicating? If we can do the job, then we should get something that, when supplemented with necessity, yields the notion of essence. This suggests that we should be able to find contingent cases of such asymmetric intrinsicality. And so that now seems to be the big question, if we're wondering whether essence should be accounted for in terms of necessity and something else, or the other way around. (Or at least whether intrinsicality should be involved if we pursue the first strategy.)

Thinking about parts of things, where those things could nevertheless have had different parts, may be one way of looking. For instance, perhaps 'My laptop contains the chip C' provides such an example. If the chip is intrinsic to the laptop, then we can say that the laptop intrinsically contains the chip, but that the chip is not intrinsically inside the laptop. But the laptop could have had another chip or perhaps no chip in that place, so it does not contain the chip necessarily.

I wonder how solid and convincing this sort of example is, though, and I wonder if there are other sorts available.