This paper considers the extension of the standard GPC algorithm to include input rate, magnitude and output constraints using the Quadratic Programing (QP) approach on a derived nonlinear multivariable anaesthesia model comprising simultaneous control of muscle relaxation (paralysis) and unconsciousness (in terms of blood pressure measurements). Simulation results, which are presented, analysed and discussed, demonstrate the superiority of the extended version in the deterministic and stochastic cases even when low output prediction horizons are chosen, and also the great flexibility with respect to choosing the limits on the manipulated as well as the output variables. The study also reveals that when heavy external disturbances occur, the algorithm, which combines input and output constraints, performs better than either the unconstrained one or the one that includes only input constraints. Under extreme conditions, the same algorithm reduces to an algorithm with only input constraints when the phenomenon of constraints incompatibilty occurs.