We highlight the potential of model predictive control (MPC) in precision manufacturing by considering the application to multistage processing machines that combine actuators with different operating ranges and different bandwidths to optimize the processing time, product quality, and to increase flexibility. The operation of these machines results in a constrained trajectory generation and control problem with reference-dependent constraints. We propose a design based on a spatial reference governor and a tracking MPC for real-time control of a dual stage processing machine. The method guarantees constraint satisfaction, finite time processing of a given spatial pattern, and real-time execution. Results on a real processing pattern generated using CAD-CAM are shown.