This article develops an axiom system to justify an additive representation for a preference relation ${\succsim}$ on the product ${\prod_{i=1}^{n}A_{i}}$ of extensive structures. The axiom system is basically similar to the n-component (n ≥ 3) additive conjoint structure, but the independence axiom is weakened in the system. That is, the axiom exclusively requires the independence of the order for each of single factors from fixed levels of the other factors. The introduction of a concatenation operation on each factor A i (...) makes it possible to yield a special type of restricted solvability, i.e., additive solvability and the usual cancellation on ${\prod_{i=1}^{n}A_{i}}$ . In addition, the assumption of continuity and completeness for A i implies a stronger type of solvability on A i . The additive solvability, cancellation, and stronger solvability axioms allow the weakened independence to be effective enough in constructing the additive representation. (shrink)