The ordinary rule of the Church is that one priest should only offer one Mass each day. They may be given faculties for offer Mass twice on weekdays and thrice on Sundays, should there be a pastoral need in a certain place. In fact, such faculties are pretty much the norm nowadays.
There are two days a year when priests have the right to offer three Masses as a given: All Souls Day and Christmas. On All Souls, a stipend may be taken only for the first Mass, and it is also the only one for which the priest may decide upon or accept an intention. The second Mass is to be offered for all the faithful departed, and the third for the intentions of the pope. On Christmas, as far as I know, there is no such restriction on intentions, and stipends may be accepted for all of the Masses. Another difference is that the three Masses of All Souls, should a priest decide to celebrate all of them, could be offered in succession. The three Masses of Christmas must be offered at the times of day to which they are assigned.
The Christmas situation raises some questions for me, however.
1. From the missal it seems that the 'three Masses' begin after the vigil Mass, and therefore would be the Mass at night, the Mass at dawn, and the Mass during the day. These three are the 'traditional' Masses of Christmas, i.e. midnight, dawn, and day. So my first question is that it would seem a priest could celebrate the vigil Mass, and then still be able to celebrate the three Masses of Christmas Day proper. That would be four Masses over the whole of the liturgical day. Is that still o.k.? Would it be an abuse of the tradition?
2. Traditionally, the Mass during the night was the Mass at Midnight. Now, at least in the Ordinary Form, it is only the Mass in nocte, and can be celebrated during the night prior to midnight. So, would it be o.k. to celebrate the Mass in nocte as one of the 'three traditional Masses' even if this were before midnight? In other words, if someone were taking up the traditional practice of the 'three Masses, ' ought he also to follow the traditional rubric for the time?
3. For pastoral purposes, the different readings for the Masses of Christmas may be switched around. For example, if you attend Christmas Mass at 4 or 5 pm on Christmas eve, you probably won't hear the gospel for the vigil Mass, but the gospel for the night Mass. The angels and the shepherds from St. Luke, which everyone knows if only from A Charlie Brown Christmas, just says Christmas in a much more accessible way that St. Matthew's genealogy. So let's say you were going to celebrate the vigil Mass in a parish complete the readings for the night Mass. If you were going to offer the night Mass later on privately, should you use the night readings again, back-fill the liturgy with the vigil readings, or go ahead to the readings for dawn?