David Lewis thinks that properties are just sets of possible individuals. SEP: “Lewis argues that for any set of actual and possible objects (fundamental or not), there is a property, namely the property an object has just in case it is a member of the given set.”
Kit Fine thinks that essence is an asymmetrical relationship. Specifically, it is an asymmetrical relationship between a set and its constituent(s). Although Socrates is essential to the singleton set {Socrates}, the set is not essential to Socrates. “It is no part of the essence of Socrates to belong to the singleton.” (“Essence and Modality“)
Suppose you accept both. Then no individual has any property essentially. After all, a property is a set, and it is not part of the essence of any individual to belong to any set. Moreover, every property has its bearers essentially. After all, constituents of a set are essential to that set. On the face of it, that is pretty weird.
Ways to get out: (1) Most obviously, don’t put Lewis and Fine together. (2) Clarify what Fine says, so that the essence relationships hold for some sets but not others. (3) Clarify what Lewis says, so properties aren’t just sets, but in some sense correspond to them. Both (2) and (3) look ad hoc to me, so perhaps the weirdness can count as an incompatibility result between Lewis and Fine?