I've previously argued that consequentialist moral theories respect the "separateness of persons" when they recognize individual persons as being of distinct intrinsic value, rather than seeing them as mere means to the single token value of aggregate welfare. (This entails more fine-grained non-instrumental desires, and associated emotions like regret, but doesn't ultimately affect what actions are the right ones to perform.) So I was interested to come across a different conception of the separateness of persons in Michael Otsuka's 'Prioritarianism and the Separateness of Persons'. According to Otsuka, a theory respects the separateness of persons when it is sensitive to "competing claims" and so treats "non-identity" cases differently:
It is morally relevant that there are distinct persons with competing claims to receive benefits. Such competing claims ground moral complaints on the part of those who would be worse off, relative to others, and the case for giving benefits to people with such complaints is stronger than it otherwise would be in analogous [intra-personal or non-identity] cases in which the prioritarian value of distributing goods in one way rather than another is equally great, yet such complaints are lacking. (371-2)