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Detecting rare diseases often requires data from multiple institutions due to the scarcity of cases at individual hospitals. Centralizing data is not feasible due to privacy, consent, and jurisdictional issues. Federated learning enables model training across hospitals without transferring raw data, but it lacks formal privacy guarantees. Model updates can still leak information, and aggregation servers may compromise privacy if they handle unprotected data. This article presents a conceptual framework combining federated learning, differential privacy, and secure multi-party computation for rare disease detection across 50+ international hospitals. The system addresses data scarcity, regulatory fragmentation, and network heterogeneity. Each hospital trains a local model, applies differential privacy to updates, and shares encrypted updates via an aggregation protocol. Non-colluding servers compute global updates without accessing plaintext data. Differential privacy reduces the impact of individual patient data, while secure multi-party computation ensures privacy at the aggregation layer. These methods enable a privacy-preserving approach to federated learning for rare disease collaboration. The proposed framework enables multi-continental rare disease detection without centralizing patient data, offering a privacy-preserving model for future consortia.