The interassociates of the free commutative semigroup on n generators, for n > 1, are identified. For fixed n, let (S, ·) denote this semigroup. We show that every interassociate can be written in the form \((S, \ast_{\bar{k}})\), depending only on a n-tuple \(\bar{k}=( k_1, \ldots, k_n)\). Next, if \((S, \ast_{\bar{k}})\) and \((S, \ast_{\bar{\ell}})\) are isomorphic interassociates of (S, ·) such that \(\phi(x_i) = x_j\), for xii and xj in the generating set of S, then \(k_i = \ell_j\). Moreover, \((S, \ast_{\bar{k}})\cong(S,\ast_{\bar{\ell}})\) if and only if \({\{k_i\}_{i = 1}^n}\) is a permutation of \({\{\ell_i\}_{i = 1}^n}\).