The answer to your question depends on how one spells out certain supplementation intuitions about composites. This can be done in precise terms in mereology, a theory (or rather class of theories) dealing with the parthood relation.
Intuitions first: The supplementation intuition says that a composite, i.e. a whole having proper parts (parts distinct from the whole) cannot consist of a single proper part. In other words proper parts are always 'supplemented' by certain other proper parts.
This intuition can be formalized in a first-order theory whose signature only contains = and the two place relation symbol P representing the parthood relation. The first three axioms capture the intuition that parthood is a partial order:
- ∀xyz(Pxy & Pyz → Pxz)
- ∀xy(Pxy & Pyx → x = y)
Now one quite strong way to represent the supplementation intuition is by adding the axiom
- ∀xy(¬Pyx → ∃z(Pzy ∧ ¬Ozx))
where Oxy := ∃z(Pzx & Pzy) ('x and y overlap' in the sense of sharing some part). This axiom says that in case y is no part of x there is some part of y such that this part and x do not overlap. Lets call 1.-4. extensional mereology (EM). Now it is easily seen that 4. and so EM entails
- ∀xy(PPxy → ∃z(Pzy ∧ ¬Ozx))
where PPxy := Pxy & x ≠ y. 5. seems to be a proper rendering of the supplementation intuition. But EM also entails that composites having exactly the same proper parts cannot be distinguished:
- ∀xy(∃zPPzx ∨ ∃zPPzy) → (x=y ↔ ∀z(PPzx ↔ PPzy)).
So, as long as your chosen mereology contains 4. it is extensional in the sense that composites are nothing more than their proper parts.