In the realm of music AI, arranging rich and structured multi-track accompaniments from a simple lead sheet presents significant challenges. Such challenges include maintaining track cohesion, ensuring long-term coherence, and optimizing 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 generated by infusing orchestral function styles into the piano arrangement. Our key design is the use of vector quantization and a unique multi-stream Transformer to model the long-term flow of the orchestration style, which enables flexible, controllable, and structured music generation. Experiments show that by factorizing the arrangement task into interpretable sub-stages, our approach enhances generative capacity while improving efficiency. Additionally, our system supports a variety of music genres and provides style control at different composition hierarchies. We further show that our system achieves superior coherence, structure, and overall arrangement quality compared to existing baselines.