Large Language Models (LLMs) deployed in enterprise settings (e.g., as Microsoft 365 Copilot) face novel security challenges. One critical threat is prompt inference attacks: adversaries chain together seemingly benign prompts to gradually extract confidential data. In this paper, we present a comprehensive study of multi-stage prompt inference attacks in an enterprise LLM context. We simulate realistic attack scenarios where an attacker uses mild-mannered queries and indirect prompt injections to exploit an LLM integrated with private corporate data. We develop a formal threat model for these multi-turn inference attacks and analyze them using probability theory, optimization frameworks, and information-theoretic leakage bounds. The attacks are shown to reliably exfiltrate sensitive information from the LLM's context (e.g., internal SharePoint documents or emails), even when standard safety measures are in place. We propose and evaluate defenses to counter such attacks, including statistical anomaly detection, fine-grained access control, prompt sanitization techniques, and architectural modifications to LLM deployment. Each defense is supported by mathematical analysis or experimental simulation. For example, we derive bounds on information leakage under differential privacy-based training and demonstrate an anomaly detection method that flags multi-turn attacks with high AUC. We also introduce an approach called "spotlighting" that uses input transformations to isolate untrusted prompt content, reducing attack success by an order of magnitude. Finally, we provide a formal proof of concept and empirical validation for a combined defense-in-depth strategy. Our work highlights that securing LLMs in enterprise settings requires moving beyond single-turn prompt filtering toward a holistic, multi-stage perspective on both attacks and defenses.