Vertical federated learning (VFL) enables parties with different features to collaboratively develop models on overlapping samples without directly sharing raw data. Conventional VFL systems typically require data overlap among all parties to perform training and inference. Recent work has relaxed this assumption to allow federated inference on non-overlapping samples. However, current methods struggle to handle scenarios where the active party only shares sample overlap with a subset of passive parties, thereby missing critical feature information from non-overlapping parties. We introduce Vertical Federated Learning Across Second-hop Parties (VFL-ASP), an enhanced VFL framework that improves feature utilization across second-hop passive parties. These parties share sample overlap with first-hop passive parties, which directly overlap with the active party. VFL-ASP extracts hidden embeddings from overlapping samples among the first and second-hop parties under encrypted federation and learns embedding approximations, which are then utilized alongside active party data to construct a VFL system. We apply knowledge distillation to refine a student model with soft labels from the VFL teacher, enabling local processing of non-overlapping data. Our evaluation on three real-world datasets demonstrates that VFL-ASP achieves improved performance over traditional VFL baselines.