I briefly looked at the patents that I could find. I see a description of a method that employs two linear transfer functions and a non-linearity to create a 'profile'. It seems to me that a post processing algorithm is possible to create an improvement in the gain function across the full range of a set of profiles, but I have not seen mention of this in the patents that I ran across.
Modeling methods directly account for non-linearities in the amplifier stages. This is one big difference between modelling and profiling. I'm a Kemper owner and use, so I know which method I prefer. The side-effect of these differences might be the behaviour of the gain knob in question.