Interestingly the discussions at the Object-Oriented event and my current enthusiasm for a possible Millnong project led me back to the old preoccupations from the time of my 2008 black book. There I draw both on Kripke's move away from descriptivism and from Lévinas' move away from thought that does no more than fit the other on the same. In both cases, there is an appeal to an other beyond our descriptive thought - some kind of transcendent other. It brings back Meillassoux to my mind, when he insists on making room for the different in nature that cannot blend into a monism of the all too human.
I think most process philosophies – including the ontology of fragments – can be seen as having problems with the transcendent other. One possible line to take is to exorcise the craving. I myself feel the attraction of a transcendent other – and the craving for some room for that is in the kernel of my sympathy towards Kripke (and to Lévinas, and to Meillassoux). But I'll try to exorcise the craving in two different directions here – and I want to make clear that I think the second is promising, even though the first way of exorcising the craving can be eventually effective.
The first line I thought was to try and take the craving from a transcendent other as a left over from creationism. It could be compared to absolutely different species. In a Darwinian nature, there is no species that is absolutely different from all others. Otherness is never complete – nothing is fully outer, just as there is no all-pervasive doubts. Doubt has to be held by belief, otherness is intimately intertwined in sameness. It is not about reducing the other to the same, but it is about finding relations (of the very kind Lévinas would call metaphysical as opposed to ontological) that tie the other to the same. The absence of absolute other could provide room for singularities taken as unique measures of sameness and otherness. In other words, maybe process philosophy would just have resources enough to exorcise the absolute other without falling prey of the idea that everything belongs in a single whole, in a cosmic blob.
The second line is to think that the open horizon of life that made us postulate well-constituted individuals provide is never complete. So, if we say with Kripke that Socrates could have gone away from philosophy, we also say would have to say that he could not go away from individuality (not from his socraticity, because I understand Kripke wants to distance himself from Russell and Quine, but from the fact that he is in one well-defined piece, one identity). But if we allow the different pieces of Socrates to have each an open horizon of life, then we loose our capacity to hold on to them in thought (to refer to them). This is indeed a predicament. However, maybe there is a way out if we just follow this thought: different things are to be kept fixed in order for other things to change. We can elaborate this by saying that reference is always with respect of a frame of reference, a background of constant posits. In one use, it could be Socrates, but in other uses it could be the philosopher who lived in Athens and impressed Plato – that could have been, say, Democritus. That description – in a somehow referential use – has an (modally) open horizon of life ahead of it. I reckon this doesn't make me into a two-dimensionalist. In fact, I think this is the thrust of Kripke's remark that possible worlds are not foreign countries or distant planets; it is from something fixed in the actual world that we relate to possible worlds. Something fixed is what is needed in order to preserve a (modally) open horizon of life, it doesn't have to be anything that is there once and for all. The need for a (modally) open horizon of life requires nothing but some fixity to be postulated in the ontology (and nothing fixed).
The second line does the trick for me, at least right now. I think the crave fro otherness doesn't have to lead to an ontology of fixed others, individuated once and for all.