Knowledge-intensive visual question answering (VQA) requires external knowledge beyond image content, demanding precise visual grounding and coherent integration of visual and textual information. Although multimodal retrieval-augmented generation has achieved notable advances by incorporating external knowledge bases, existing approaches largely adopt single-pass frameworks that often fail to acquire sufficient knowledge and lack mechanisms to revise misdirected reasoning. We propose PMSR (Progressive Multimodal Search and Reasoning), a framework that progressively constructs a structured reasoning trajectory to enhance both knowledge acquisition and synthesis. PMSR uses dual-scope queries conditioned on both the latest record and the trajectory to retrieve diverse knowledge from heterogeneous knowledge bases. The retrieved evidence is then synthesized into compact records via compositional reasoning. This design facilitates controlled iterative refinement, which supports more stable reasoning trajectories with reduced error propagation. Extensive experiments across six diverse benchmarks (Encyclopedic-VQA, InfoSeek, MMSearch, LiveVQA, FVQA, and OK-VQA) demonstrate that PMSR consistently improves both retrieval recall and end-to-end answer accuracy.