In the realm of music AI, arranging rich and structured multi-track accompaniments from a simple lead sheet poses significant challenges in context coherency, music creativity, and computational efficiency. In this paper, we introduce a novel system that leverages prior modelling over disentangled style factors to address these challenges. Our method presents a two-stage process: initially, a piano arrangement is derived from the lead sheet by retrieving piano texture styles; subsequently, a multi-track orchestration is achieved by infusing orchestral function styles into the piano arrangement. The key design is to employ vector quantization and a unique multi-stream Transformer to model the long-term flow of orchestration style, leading to flexible and controllable music generation. Experiments show that by factorizing the arrangement task into interpretable sub-stages, our approach enhances generative capacity. Additionally, the system supports varied music genres and provides style control at different compositional hierarchies. Lastly, we demonstrate that our system delivers superior arrangement quality over existing baseline methods.