Object search is a fundamental task for robots deployed in indoor building environments, yet challenges arise due to observation instability, especially for open-vocabulary models. While foundation models (LLMs/VLMs) enable reasoning about object locations even without direct visibility, the ability to recover from failures and replan remains crucial. The Multi-Object Search (MOS) problem further increases complexity, requiring the tracking multiple objects and thorough exploration in novel environments, making observation uncertainty a significant obstacle. To address these challenges, we propose a framework integrating VLM-based reasoning, frontier-based exploration, and a Partially Observable Markov Decision Process (POMDP) framework to solve the MOS problem in novel environments. VLM enhances search efficiency by inferring object-environment relationships, frontier-based exploration guides navigation in unknown spaces, and POMDP models observation uncertainty, allowing recovery from failures in occlusion and cluttered environments. We evaluate our framework on 120 simulated scenarios across several Habitat-Matterport3D (HM3D) scenes and a real-world robot experiment in a 50-square-meter office, demonstrating significant improvements in both efficiency and success rate over baseline methods.