Traditional banking, which relies on relationship managers to provide personalized financial advice, recommend products and assess risk, has been left relatively untouched from potential enhancements of Generative AI. In this work, we propose - EAGLE, a multi-agent system for this task, which automates banking recommendations while incorporating real-time, risk-aware financial planning and augments and enhances operations by cutting down on time taken for research on customer profiles, products, financial plans as well as call handling. Through simulated experiments and novel proposed metrics, we establish robust performance on this task using our framework. Our proposed multi-agent system enhances personalization of products recommendation, enables risk-aware financial planning and asset allocation, as well as establishes a foundation for next-generation banking systems.