This paper introduces CAFE-MPC, a cascaded-fidelity model predictive control framework for on-the-fly synthesis of complex dynamic maneuvers in legged robots. The framework uses a cascaded-fidelity model predictive controller (CAFE-MPC) that strategically relaxes the planning problem along the prediction horizon to improve computational and performance efficiency. The CAFE-MPC is solved using an efficient customized multiple-shooting iLQR (MS-iLQR) solver tailored for hybrid systems. The action-value function from CAFE-MPC is used as the basis for a new value-function-based whole-body control (VWBC) technique that avoids additional tuning for whole-body control (WBC). The proposed framework unifies whole-body MPC and conventional whole-body quadratic programming (QP), which have been treated as separate components in previous works. The framework enables accomplishing gymnastic-style running barrel roll on the MIT Mini Cheetah for the first time. The CAFE-MPC also advances the performance of whole-body MPC without necessarily increasing computational cost. The proposed VWBC shows superior performance over the Riccati feedback controller in terms of constraint handling. The framework is built upon model predictive control (MPC), which produces control inputs by predicting the future behavior of the robot as part of solving a trajectory optimization (TO) problem. The framework unlocks on-the-fly synthesis of gymnastic running barrel roll by simply specifying an input reference motion without further tuning of the system parameters. The framework is structured as an optimization-based control framework that takes a reference trajectory as input and outputs commands directly executable on the robot. The framework includes a motion compiler consisting of CAFE-MPC, a customized MS-iLQR solver for numerical optimization, and the VWBC. The MS-iLQR solver is used for both offline TO and online MPC. The framework is tested on the MIT Mini Cheetah, achieving a running barrel roll in the middle of running. The framework is also shown to be effective for other complex tasks. The paper discusses the contributions of the work, including the development of CAFE-MPC, the extension of multiple-shooting iLQR to hybrid systems, the development of a value-function-based whole-body controller (VWBC), and the overall optimization-based control framework. The paper also discusses related work in the areas of MPC for legged robots, numerical optimization for MPC, whole-body control, and reinforcement learning for legged robots. The paper concludes with a discussion of the limitations of the work and suggestions for future research.This paper introduces CAFE-MPC, a cascaded-fidelity model predictive control framework for on-the-fly synthesis of complex dynamic maneuvers in legged robots. The framework uses a cascaded-fidelity model predictive controller (CAFE-MPC) that strategically relaxes the planning problem along the prediction horizon to improve computational and performance efficiency. The CAFE-MPC is solved using an efficient customized multiple-shooting iLQR (MS-iLQR) solver tailored for hybrid systems. The action-value function from CAFE-MPC is used as the basis for a new value-function-based whole-body control (VWBC) technique that avoids additional tuning for whole-body control (WBC). The proposed framework unifies whole-body MPC and conventional whole-body quadratic programming (QP), which have been treated as separate components in previous works. The framework enables accomplishing gymnastic-style running barrel roll on the MIT Mini Cheetah for the first time. The CAFE-MPC also advances the performance of whole-body MPC without necessarily increasing computational cost. The proposed VWBC shows superior performance over the Riccati feedback controller in terms of constraint handling. The framework is built upon model predictive control (MPC), which produces control inputs by predicting the future behavior of the robot as part of solving a trajectory optimization (TO) problem. The framework unlocks on-the-fly synthesis of gymnastic running barrel roll by simply specifying an input reference motion without further tuning of the system parameters. The framework is structured as an optimization-based control framework that takes a reference trajectory as input and outputs commands directly executable on the robot. The framework includes a motion compiler consisting of CAFE-MPC, a customized MS-iLQR solver for numerical optimization, and the VWBC. The MS-iLQR solver is used for both offline TO and online MPC. The framework is tested on the MIT Mini Cheetah, achieving a running barrel roll in the middle of running. The framework is also shown to be effective for other complex tasks. The paper discusses the contributions of the work, including the development of CAFE-MPC, the extension of multiple-shooting iLQR to hybrid systems, the development of a value-function-based whole-body controller (VWBC), and the overall optimization-based control framework. The paper also discusses related work in the areas of MPC for legged robots, numerical optimization for MPC, whole-body control, and reinforcement learning for legged robots. The paper concludes with a discussion of the limitations of the work and suggestions for future research.