It depends on what you mean by "possible." :-) If you're using a fit program in the SimBiology Model Analyzer app or the functions sbiofit or sbiofitmixed (which are the same functions used by this program), then you do not have direct control over the objective function. You do have indirect control of the objective function by configuring the Weights or ErrorModel options.
If you want complete control over the objective function, you can create a custom program in the app or write your own function at the command line. If you want to take this approach, I recommend creating a SimFunction from the model. (That's actually what sbiofit and sbiofitmixed do internally.) The SimFunction object makes it easy to efficiently do many simulations at different parameter values.
