In response to the original question, priests who are religious (regular clerics) must follow the constitutions of their respective religious institutes. If the constitutions allow for the celebration of the EF, then it can be done without the permission of the superior.
I can speak best about the Franciscan tradition. In our family, the rule is very clear that priests do not enjoy special privileges, because they are priests. This includes the assumed right to celebrate mass. St. Francis, who was not a priest, was very specific that in a house where there is more than one priest, only one priest may be allowed to celebrate mass. There is no private mass in a side altar or side chapel as is the custom in clerical communities (orders of priests). Franciscans were not founded as an order of priests, as are the Carmelites and Dominicans. They are orders of priests or clerical institutes.
It is up to the successor of St. Francis to grant permission for the celebration of mass. In most houses, the superiors allow the ordained to concelebrate. The celebration of mass alone is discouraged, not because the mass is bad, but because our priests are to be brothers first. Therefore, they should always pray with their brothers. That being said, there are times when an ordained friar cannot be present for the conventual mass and superiors do not prohibit the celebration of mass alone. We (Franciscans) do not use the term “private mass.” That’s why I say, mass alone. It is the teaching of St. Francis that mass is never private, even when it’s only the priest. The mass and the Divine Office are the prayer of the Church. It is always public. The Holy Father used the term “private” in SP to mean alone, not PRIVATE.
Back to the rest of the question. There is one Franciscan congregation that has permission to celebrate the EF as its conventual mass, the Franciscans of the Immaculate. This was allowed, because it served the spiritual needs of the brethren. In the other congregations of the Order, the EF can be celebrated, but it is reserved for special occasions, to meet the needs of the brethren, if necessary and always with the permission of the major superior. For example, at Franciscan University, some students and faculty asked for the EF. The Major Superior was consulted and he gave permission for it to be done. It is not the conventual mass. This does not mean that it cannot be celebrated for the friars as well. What it means is that it cannot become the usual and customary form. That would require all kinds of votes and permissions, because the form is extraordinary.
All this being said, Franciscans cannot limit themselves to celebrating the EF. Even the Franciscans of the Immaculate, who have permission to celebrate the conventual mass using the EF, may not limit themselves to the EF, unlike the SSPX or the FSSP. If a Franciscan celebrates for the community, he must comply with the superior. If he celebrates for a parish, he must comply with both: superior and local bishop. In addition, the brothers in the house may vote on the matter. Everyone is bound to the decision of the vote. It’s part of the vow of obedience, which does not bind diocesan priests. They have no local community or major superior to govern them or their liturgical life. The bishop only controls what they do in ministry, not in private. In the case of religious, the founder, the rule, the constitutions, the Major Superior and the chapter, harmoniously govern your entire life. Legally speaking, yes a Major Superior can prohibit the celebration of the EF, despite the permission granted by SP.
There is a technicality that most lay people don’t know about. The Holy Father was very astute. In SP he writes that regular and secular priests may celebrate the EF in private and that religious need permission to celebrate it as the conventual mass. What the Holy Father deliberately did not address, so as not to rock the boat, is the fact that in some communities, religious may not celebrate mass alone. Therefore, only those religious who are allowed to celebrate mass alone can celebrate the EF in private.
Fraternally,
Br. JR, OSF
Since we don’t have the right books.