You can't calculate IPn without Nonlinear Model.S-Parameters carry NO information about Nonlinearity.
Essentially, you cannot calculate ANY kind of Nonlinearity of an Active Device since you don't know the Degree of Nonlinearity , you can just simulate with a given Nonlinear Model in a serious simulator.
Either you will implement this circuit and measure OR you will extract Nonlinearity of this active device. It's almost impossible to extract these coefficients because it needs highly qualified engineering experience.