Another relation is strictly connected to parthood: the relation that connects many things to a single thing that includes whatever is in the many things and nothing extraneous to them; this many-one relation can be dubbed composition.
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The thesis is that there is a single, general, exhaustive theory of parthood and composition. This theory, usually called Classical Extensional Mereology
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(a) parthood is transitive (if a first thing is part of a second thing, and this second thing is part of a third thing, then the first thing is part of the third as well);
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(b) given some things, there is at most one thing composed by them;
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(c) given some things, no matter how heterogeneous and disparate they are, there is at least one thing composed by them.
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Consider, as a first example, the essential/accidental distinction.
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Are some parts of a whole such that their annihilation would annihilate the whole too?
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Another example: the supervenience or emergence of the properties of complex entities over the properties and relation of their parts.
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According to the narrow understanding of mereology as a discipline I am going to adopt, essentiality, dependence, and supervenience lie beyond the explanatory scope of mereology.
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Mereology is only about the formal features of the relation of parthood, and about identity and existence conditions for wholes.