Let's agree that there is the property of being such and such, where such and such is a particular object, and be agnostic for a moment about whether that property is a fundamental property or derivative somehow. At the same time, let's acknowledge the long-standing distinction between intrinsic properties and extrinsic properties, where whether an intrinsic property applies to some object depends only on how that object is, in some to-be-specified sense. Do you think that the property of being such and such is an intrinsic property, an extrinsic property, or sometimes one sometimes the other?
To which I responded:
I lean towards the extrinsic option (insofar as I have a grasp of the question at all). At least for 3-Dists, the best theory of identity is Nozick's "closest continuant" account, but which future object is the closest continuant of your present self is an extrinsic matter. (Fission cases illustrate this nicely. Either continuant alone would have been such-and-such, were it not for the other!) And counterpart theorists are going to say similar things about trans-world identity. I can't tell whether a counterfactual guy is Jack just by looking at him; I need to know whether there are any better candidates in the vicinity!
How might a world ontologist accommodate some kind of (derivative) 'thisness'? We've seen it must be extrinsic, because there is nothing in the duplicates Bob1 and Bob2 to distinguish them. But it's not entirely obvious how to fill out the details. My basic strategy is to model the identity facts on the semantic facts, as per the holistic account I offer here. Roughly: the distinct identities [thisnesses] of Bob1 and Bob2 consists in the extrinsic fact that their world contains two Bob-like duplicates. The perfect symmetry means that there are no grounds for assigning any particular distinct property to either one of them alone -- giving just one of them the peculiar property of being Bob1, say. That's no more possible than our name 'Bob1' referring to a determinate one of the two. Nonetheless, it may be determinate that 'Bob1' and 'Bob2' do not co-refer, and similarly that being Bob1 and being Bob2 are not co-exemplified, even if there's no further fact about which thisness is where. Does that seem objectionable? (It would be if these vague properties were metaphysically fundamental. But I think their 'derivative' status may afford more leeway...)