Based on the concepts of composition ring and composition hyperring, in this note we introduce the notion of composition structure for (m, n)-hyperrings and study the connections with composition hyperrings. Moreover we show that particular strong endomorphisms of (m, n)-hyperrings can determine the composition structure of a such (m, n)-hyperrings. Finally, the three isomorphism theorems are presented in the case of composition (m, n)-hyperrings, showing that they are not a pure extension of those for composition hyperrings.