I have the good of friendship with Trent. Suppose Trent was my only friend. Then I would be getting two good things out of my friendship:
- having Trent as a friend
- having a friend.
So the family of friendship-with-X goods has the property that not only are particular members of the family non-instrumentally valuable, but it's also of non-instrumental value to possess some member or other of that family, which gives one d over and beyond that particular member. Not all families of goods are like this. Consider the family F consisting of the two goods (a) friendship with Trent and (b) reading Anna Karenina. There is no good of possessing some member of F that goes over and beyond the two particular goods in F. It's good to be friends with Trent and it's good to read Anna Karenina, but there is no third disjunctive good here. Or at least there is no third non-instrumental disjunctive good (we can imagine cases where the disjunction is, as such, instrumentally valuable, say when a prize is given to anyone who is friends with Trent or is reading Anna Karenina).
Here's another example. Consider the subfamily of the friendship-with-X goods given by friendships with blue-eyed people. While every member of this subfamily is valuable (I'm supposing for simplicity that all cases of friendship are valuable), there does not seem to be a further value to being friends with a blue-eyed person. Someone all of whose friends are brown- or green-eyed is missing out on the good of friendship with the particular people whose eyes are blue, but isn't losing out on some further good. On the other hand, someone who has no female (or no male or no American or no Iranian) friends seems to be losing out on something valuable over and beyond the value of the particular female friends that he or she does not have, though it is unclear whether the lost value here is instrumental (say by providing a different outlook on the world) or not.