To understand Nagasena's argument you must first understand that things (subjects of discourse or thought) are, in reality, universes of discourse. That is to say, they are sets of defining characteristics that are bound together by a term or designation. The term 'chariot', for example, is: 'a two-wheeled horse-drawn battle car of ancient times used also in processions and races.' Those objects in the world that we call 'chariots' are so called only in virtue of the fact that they exhibit that set of characteristics which are expressed in the definition of the term.

Now, every universe of discourse comprises a both 'relation' and a set of things (called 'relata') between which that relation is said to hold, the relation being that which turns the many (relata) into one – hence the term 'universe' (literally 'turned into one'). Unlike the relata (wheels, axle, etc.), which are concrete entities, the relation which binds them is an abstract entity. Thus, if we take a chariot apart, the chariot is not to be found in any one of its parts or in the sum of its parts. It is only when the chariots parts are assembled in the appropriate manner, does the chariot come into being.

The ancient essentialists called these two aspect of a thing its 'form' (relation) and its 'matter' (relata). In Buddhist terms they were called its operative cause (relation) and constitutive cause (relata). That the relation (thing itself) is primal is evidenced by the fact that a 'universe' is also called a 'domain' which connotes the complementary concepts of a property-bearer (relation) and its properties (relata).
Hope you find this helpful.

Thank you, Jehu.
This certainly adds clarity to my initial readings, and you've provided some more light for me. I think i was, wrongly, trying to defeat Nagasena's argument through a pluralist argument whereas i should focus on sustaining the criticism instead. I think, for now, I will try to push back on one of the premises, namely: that the chariot cannot be anything else, other than the parts or sum.