Graph Neural Networks (GNNs) extend deep learning techniques to non-Euclidean domains, designed specifically to process node, edge, and structural information in graph-structured data. Spectral Graph Neural Networks (Spectral GNNs) leverage the spectral decomposition of the graph Laplacian to extract both global and local features in the frequency domain. Building upon the foundational CayleyNet framework, we propose the Next Generation CayleyNet. Our model introduces the second spectral zoom parameter a； the original spectral zoom parameter h determines the extent of spectral magnification, controlling the resolution of the target frequency band, while the newly introduced a defines the focal point within the spectrum. Through the synergistic use of these parameters, the model enables multi-scale feature extraction and enhances its capability for localized spectral analysis. Additionally, we explore alternative numerical implementations of the Cayley shift operator, including the Lanczos method, which facilitates the storage of eigen decomposition results. This capability is particularly advantageous for large-scale graphs, as it allows efficient reuse of spectral information during filtering. Advisor: Dr. Ron Levie