An interconnection network is an inevitable component for constructing parallel computers. It connects computation nodes so that the nodes can communicate with each other. As a parallel computation essentially requires inter-node communication according to a parallel algorithm, the interconnection network plays an important role in terms of communication performance. This paper focuses on the collective communication that is frequently performed in parallel computation and this paper addresses the Cup-Stacking method that is proposed in our preceding work. The key issues of the method are splitting a large packet into slices, re-shaping the slice, and stacking the slices, in a genetic algorithm (GA) manner. This paper discusses extending the Cup-Stacking method by introducing additional items (genes) and proposes the extended Cup-Stacking method. Furthermore, this paper places comprehensive discussions on the drawbacks and further optimization of the method. Evaluation results reveal the effectiveness of the extended method, where the proposed method achieves at most seven percent improvement in duration time over the former Cup-Stacking method.