Composition as general identity

Here are three main challenges defenders of composition as identity: the Syntactic Challenge, the Semantic Challenge, and the Discernability Challenge.
In the paper, the author claims all three challenges can be met. The first — van Inwagen’s Syntactic Challenge — is that the view cannot be expressed grammatically in English. The author responds by appealing to free relatives as operators that shift syntactic number while leaving semantic number fixed. The second — Lewis’s Semantic Challenge — is that no generalization of standard notions of identity can be put in service of composition as identity. The author responds by giving full set-theoretic models of a generalized identity relation that preserves standard singular and plural identity. The author also derives a generalization of the part-hood relation that preserves classical extensional mereology, and shows that standard features of plural logic are preserved. The third — Lewis’s Discernability Challenge — is that one cannot account for apparent failures of Leibniz’s Law. This challenge is met by utilizing two different cover-based semantics for predication in plural logic involving no restrictions on Leibniz’s Law for general identity. Sider’s recent objections are addressed. A technical appendix gives relevant results.