Graph theory provides a mathematical framework for modeling relationships among entities viavertices (nodes) and edges [1, 2]. A hypergraph extends this framework by allowing hyperedges to connectany number of vertices, thereby capturing complex multi-way interactions [3]. The SuperHyperGraph conceptgeneralizes hypergraphs further through iterated power-set constructions and has recently drawn significantresearch interest [4, 5].Graph Neural Networks (GNNs) propagate and aggregate node features across graph topologies via learn-able message-passing to capture structural context [6–8]. Extensions such as Hypergraph Neural Networks,SuperHyperGraph Neural Networks, Multigraph Neural Networks, and MultiHyperGraph Neural Networkshave likewise been explored [9, 10].In this paper, we introduce and analyze the Multi n-SuperHyperGraph Neural Network, a theoretical extensionof SuperHyperGraph Neural Networks built upon Multi-SuperHyperGraph structures. We expect that thisframework will stimulate further advances in the study and application of GNNs