Biometric recognition plays an increasingly pivotal role in cybersecurity, where the CIA triad, Confidentiality, Integrity, and Availability, forms the cornerstone of information security, with authentication as a critical yet challenging component. This paper presents the Biometric Multi-modal Authentication System using Geometric Programming (BMMA-GPT), tailored for deployment in Fast IDentity Online (FIDO/FIDO2)-enabled environments and Zero Trust Architectures (ZTA). The system employs a dual-threshold mechanism integrated with Defense-in-Depth (DiD) strategies to simultaneously enhance accuracy, efficiency, and security. The underlying optimization problem is formulated as a mathematical programming task and reformulated into a Geometric Programming (GP) model to efficiently compute optimal biometric permutations and verification thresholds under constrained estimation errors. BMMA-GPT enables the flexible integration of multiple biometric modalities, allowing dynamic adjustments to meet both individual user profiles and organizational security requirements. It achieves a high Area Under Curve (AUC) of approximately 0.99 while maintaining authentication latency under 1.5 seconds. This design supports Chief Information Security Officers (CISOs) in configuring tailored authentication processes with minimal computational cost, enhancing resilience against spoofing attacks and ensuring seamless user experience. By aligning biometric verification with DiD principles and GP-based optimization, the proposed framework offers a scalable and robust solution for identity authentication in complex digital ecosystems.