Constituent ontologists hold that objects are in some sense 'built up' from metaphysically more basic constituents (e.g. properties). Michael Loux's Principle of Constituent Identity (PCI) states that if X and Y have all the same constituents (in the same arrangement), they must be one and the same object.
But now consider our old friends, duplicates Bob1 and Bob2 in the symmetrical universe. They are qualitatively indiscernible, both intrinsically and even when we take relational properties into account. So, we might wonder, in virtue of what are they distinct? We would seem driven to posit haecceities, primitive 'thisness' or bare identity; one has the fundamental property of being Bob1 - and the other, being Bob2 - and that's what sets the two of them apart. (Robert Adams argues along these lines in his 1979 classic, 'Primitive Thisness and Primitive Identity'.)
I find this a pretty unsatisfying solution, myself. Instead, I take the possibility of "indiscernibles" to show that the whole world is metaphysically prior to its parts. We should reject PCI: there's nothing in the isolated individuals Bob1 and Bob2 that would tell you that they are two in number rather than one and the same. Instead, it is fundamental fact about the world as a whole that it contains two Bobs and not just one.
Actually, even this is not quite right, for the fundamental description of the world shouldn't engage in explicit counting. It's conceivable that there is no uniquely correct answer to the question how many objects there are in the world. For example, Ian Hacking has suggested that there may be no difference between a world containing one iron sphere in a space which curves back on itself vs. two spheres in Euclidian space. We may just have these two ways of describing one and the same possibility. At least, we shouldn't rule this out from the start. Ultimately, though, I think we can reach the conclusion that these are distinct possibilities, via the counterfactual facts (which I'm more tempted to take as primitive). In the one-sphere /curved-space world, it's a fact that if God were to turn the one sphere to gold, then any sphere accessible from this point would also be gold. But the two-sphere world is clearly different: if one were turned to gold, there would remain an iron sphere in the distance.
I do have a curious bullet to bite here nonetheless: you might initially think that there are two possible ways for God to turn an iron sphere to gold in the two-sphere world. He can turn the one sphere to gold, or else the other one. But as a Lewisian, I want to deny this. Possible worlds are fully described by qualitative description: one of two previously indiscernible iron globes is turned to gold. There is no sense to be made of another possibility exactly like this one but where the identities of the globes somehow switch or otherwise differ. (That would be to treat identity as an ontological primitive, which I'm loath to do.)