It is never necessary for you to fit a primary XPS peak with some chosen number of component peaks. Rather, it is always necessary that you never fit a primary XPS peak with more components than are permitted by the chemistry of the sample that you have analyzed.

With that in mind, when you sit down to analyze an XPS spectrum, you either a) know the chemistry of your sample accurately or b) want to solve for the minimum reasonable chemistry of your sample. For a), you will fit the spectrum with exactly the required components to match what you know. For b), you will fit component peaks to be self-consistent within the XPS spectrum itself. In most cases, peak-fitting of an XPS spectrum uses a bit of both these options. At the start, you know the chemistry of your sample within a reasonable degree of accuracy. During the data analysis (peak fitting), you "guess" about other components that you "think" might be on the sample. In such cases, your must absolutely avoid that you try to "out-guess" the answer and give too many peaks than can be justified.

As S. Feliu mentioned, one method to decide whether a component peak is physically realistic and therefore self-consistent for the spectrum is to cross-correlate it against other component peaks that absolutely must appear when it does. For example, the presence of a metal oxide demands a component peak in both the O1s and the metal levels. So, when you see a component peak for the metal oxide in the metal levels, you are justified to fit the O1s peak with a component for a metal oxide. OTOH, when you see absolutely no sign of a component peak for metal oxide peak in the metal levels, you can only guess (with some good reasoning) that you likely also should not include a component peak for a metal oxide in the main O1s peak. The latter case is far more nebulous than the former, as you can see.

In conclusion, the best rule stands as: Never fit a primary XPS peak with a component peak that cannot be justified "a priori" by the known chemistry of the sample itself or certified rigorously by a self-consistent analysis of all other peaks in the entire XPS spectrum.

I agree with conclusion of Jeffrey Weimer. Considering that the chemical shift observed for an atomic specie is the result of the complete atomic environment and not only depending of a particular associated bond. Therefore, also interesting to look at the Auger chemical shift which can be measured on the XPS Auger peaks.