We define a natural partial exchangeability assumption for multi-class systems with Polish state spaces, under which we extend several results for exchangeable systems. We prove that convergence within each class to an infinite i.i.d. system implies asymptotic independence between different classes, that the vector of the empirical measures of the classes is a sufficient statistic for the law of the system, that the convergence in law of this vector is equivalent to that of the system, and an extension of the Hewitt-Savage 0-1 Law.