Private Mass

[Morning_Star15]

I have heard that a “good reason” for celebrating Mass privately is not “because he wants to”, but “for his own spiritual benefit”. I suppose that could be considered a subset of the want, but it does exclude the scenario you painted above.
I don’t see how the presence of the people would prevent a priest from offering more than one Mass per day, and collecting the stipend from each…

He could also offer up that Mass for the intentions of others, not just for his own spiritual benefit. A Chaplain at my university once offered up a Novena of Masses for the intention of the students of the university, some of which were private Masses. Even without those people being present, the Mass can still benefit people other than the priest.