Fine-tuning methods such as Direct Preference Optimization (DPO) and Group Relative Policy Optimization (GRPO) have demonstrated success in training large language models (LLMs) for single-turn tasks. However, these methods fall short in multi-turn applications, such as diagnostic patient interviewing, where understanding how early conversational turns influence downstream completions and outcomes is essential. In medicine, a multi-turn perspective is critical for learning diagnostic schemas and better understanding conversation dynamics. To address this gap, I introduce Savage Conversation Forests (SCF), a reinforcement learning framework that leverages a branched conversation architecture to fine-tune LLMs for multi-turn dialogue. SCF generates multiple possible conversation continuations at each turn, enabling the model to learn how different early responses affect downstream interactions and diagnostic outcomes. In experiments simulating doctor-patient conversations, SCF with branching outperforms linear conversation architectures on diagnostic accuracy. I hypothesize that SCF's improvements stem from its ability to provide richer, interdependent training signals across conversation turns. These results suggest that a branched training architecture is an important strategy for fine tuning LLMs in complex multi-turn conversational tasks.