A true Monte Carlo analysis varies the device parameters in a random fashion, so that every combination of variations are covered. This is also what you get in production.
You don't need to vary every parameter of the device, only the major ones. Varying the threshold value, transconductance and capacitances are sufficient for a MOS device. If matching is expected, there must be two additional entries, one for the absolute variation, and one for the vairation between the devices on the same chip. These "tolerances" are either directly inseted into the model file directly or contained in a seperate file, depending on the analysis program used. The monte carlo program then simply runs the chosen analysis repetedly, each time with a different set of variations, randomly chosen.