Contouring systems involve competing control objectives of maximising accuracy while minimising traversal time. A previously developed model predictive contouring controller for biaxial systems is extended to multi-axis systems subject to joint acceleration and jerk constraints. This requires consideration of manipulator forward kinematics and both position and orientation of the end effector. The control design is based on minimising a cost function which reflects the trade-off between the control objectives. A new architecture is proposed where the joint position controllers operate at a sample rate comparable to industrial machines, while the contouring control scheme operates at a slower rate. The proposed approach is applied to a simulation model of an industrial profile cutting machine. A number of implementations are presented requiring varying degrees of modification to the existing machine hardware and sensing capability. Results demonstrate the effect of the cost function weights on contouring accuracy and traversal time, as well as the trade-off between achieving the best contouring performance and minimising modification of the existing system.