Retrieval-Augmented Generation (RAG) grounds large language model outputs in external evidence, but remains challenged on multi-hop question answering that requires long reasoning. Recent works scale RAG at inference time along two complementary dimensions: sequential depth for iterative refinement and parallel width for coverage expansion. However, naive scaling causes context contamination and scaling inefficiency, leading to diminishing or negative returns despite increased computation. To address these limitations, we propose SPARC-RAG, a framework that coordinates joint depth–width scaling around a unified context management mechanism—a shared global context state on which specialized control agents regulate parallel exploration and sequential stopping. To optimize scaling behavior, we further introduce a lightweight fine-tuning method with process-level verifiable preferences, which improves the efficiency of sequential scaling and effectiveness of parallel scaling. Across five single- and multi-hop QA benchmarks, SPARC-RAG outperforms the strongest reproduced baseline by an average of 3.8 F1 points at 7B and 9.8 at 32B, with the largest gains on challenging multi-hop tasks.