Differential privacy (DP) has been integrated into graph neural networks (GNNs) to protect sensitive structural information, e.g., edges, nodes, and associated features across various applications. A prominent approach is to perturb the message-passing process, which forms the core of most GNN architectures. However, existing methods typically incur a privacy cost that grows linearly with the number of layers (e.g., GAP published in Usenix Security’23), ultimately requiring excessive noise to maintain a reasonable privacy level. This limitation becomes particularly problematic when multi-layer GNNs, which have shown better performance than one-layer GNN, are used to process graph data with sensitive information.