Multi-agent systems of large language models (LLMs) show promise for complex reasoning, but their effectiveness is often limited by fixed collaboration protocols. These frameworks typically focus on macro-level orchestration while overlooking agents’ internal deliberative capabilities. This critical meta-cognitive blindspot treats agents as passive executors unable to adapt their strategy based on internal cognitive states like uncertainty or confidence. We introduce the Meta-Policy Deliberation Framework (MPDF), where agents learn a decentralized policy over a set of high-level meta-cognitive actions: Persist, Refine, and Concede. To overcome the instability of traditional policy gradients in this setting, we develop SoftRankPO, a novel reinforcement learning algorithm. SoftRankPO stabilizes training by shaping advantages based on the rank of rewards mapped through smooth normal quantiles, making the learning process robust to reward variance. Experiments show that MPDF with SoftRankPO achieves a a 4--5\% absolute gain in average accuracy across five mathematical and general reasoning benchmarks compared to six state-of-the-art heuristic and learning-based multi-agent reasoning algorithms. Our work presents a paradigm for learning adaptive, meta-cognitive policies for multi-agent LLM systems, shifting the focus from designing fixed protocols to learning dynamic, deliberative strategies.