You an always define your own custom model using fittype. Nothing stops you. But multiple term sums of exponential fits are often difficult to estimate well. Personally, if I was writing the curvefitting toolbox, I would leave it out too, just because most people lack good enough data or good enough starting values. So I would force the person who really wants to do that, to also know enough about what they are doing to have even a remote chance of success.
But nothing stops you from doing as you wish. As I said though, good data and good starting vaues will be crucial. If you allow it to choose its own random starting values, then expect possibly total crap for a result.