Finally, there are rites which exist within the Western Church which are attached to individual dioceses or orders. For instance:
All priests of the Diocese of Toledo, Span belong to the Mozarabic Rite, but primarily celebrate in the Roman Rite.
I’m not so sure that every priest of Toledo is considered Mozarabic. However, all priests of Braga have faculties for the Bragan Rite, although few actually use it.
All priests of the Diocese of Milan belong to the Ambrosian Rite, but primarily celebrate in the Roman Rite.
It’s true that all priests of the Archdiocese of Milan (and certain parts of the old ecclesiastical province of Milan) are of the Ambrosian Rite, but it’s necessarily so that they primarily celebrate in the Roman Rite. It depends on the individual priest, and even then, they may only do it in a church that it not designated as one of the Ambrosian Rite.
Any priest who is a member of the Order of Preachers (not including tertiaries) can celebrate the Dominican Rite (likewise with all other religious rites).
There are only a few Orders who have their own Rites: the Dominicans, the Carthusians, the Cistercians, the Carmelites, and the Norbertines. The Dominicans require permission from the Father Provincial. The Carthusians use only their own Rite. The Carmelite Rite is, unfortunately, no longer in general use since the early 1970s, (although it may, Deo volente, be experiencing a come back of sorts), while the Norbetine (O.Praem) was abandoned, by vote of the General Chapter, since shortly after Trent (and could, in theory, at least, be revived the same way since it was never formally suppressed).