Full Idea
Counterparts involve the thesis that domains of different possible worlds are disjoint: possible individuals exist in at most one possible world. This seems to suggest extreme essentialism, where nothing could differ from how it is.
Gist of Idea
If counterparts exist strictly in one world only, this seems to be extreme invariant essentialism
Source
Robert C. Stalnaker (Counterparts and Identity [1987], 2)
Book Reference
Stalnaker,Robert C.: 'Ways a World Might Be' [OUP 2003], p.118
A Reaction
He quotes Salmon (1981:236) as saying counterpart theory is particularly inflexible essentialism. This is a long way from my use of 'essentialism'. The problem is just the extent to which my counterpart is 'the same' as me.