For multi-limbed robots, motion planning with posture and force constraints tends to be a difficult optimization problem due to nonlinearities, which also present extended solve times. We propose a multi-stage optimization framework with data-driven inter-stage coupling constraints to address the nonlinearity. Both clustering and evolutionary approaches to find the McCormick envelope relaxations are used to find the problem-specific parameters. The learned constraints are then used in the prior stages, which provides advanced knowledge of the following stages. This leads to improved solve times and interpretability of the results. The planner is validated through multiple walking and climbing tasks on a 10 kg hexapod robot.