This paper presents a proof-of-concept demonstration of agent-to-agent communication across distributed systems, using only natural-language messages and without shared identifiers, structured schemas, or centralised data exchange. The prototype explores how multiple organisations (represented here as a Clinic, Insurer, and Specialist Network) can cooperate securely via pseudonymised case tokens, local data lookups, and controlled operational boundaries. The system uses Orpius as the underlying platform for multi-agent orchestration, tool execution, and privacy-preserving communication. All agents communicate through OperationRelay calls, exchanging concise natural-language summaries. Each agent operates on its own data (such as synthetic clinic records, insurance enrolment tables, and clinical guidance extracts), and none receives or reconstructs patient identity. The Clinic computes an HMAC-based pseudonymous token, the Insurer evaluates coverage rules and consults the Specialist agent, and the Specialist returns an appropriateness recommendation. The goal of this prototype is intentionally limited: to demonstrate feasibility, not to provide a clinically validated, production-ready system. No clinician review was conducted, and no evaluation beyond basic functional runs was performed. The work highlights architectural patterns, privacy considerations, and communication flows that enable distributed reasoning among specialised agents while keeping data local to each organisation. We conclude by outlining opportunities for more rigorous evaluation and future research in decentralised multi-agent systems.