Methods for multiplication of polykays have been given by various authors. Carney used ordered partitions in considering double products. In this paper, relations between polykays, symmetric means, augmented monomial functions and unrestricted power sums are studied. The method of ordered partitions is extended to obtain multiple products of polykays. Kronecker products of ordered partitions are introduced and certain rules are suggested by whose application the size of the problem is reduced considerably. The method is illustrated on triple products of weight 7.