Can. 905 §1. A priest is not permitted to celebrate the Eucharist more than once a day except in cases where the law permits him to celebrate or concelebrate more than once on the same day.In my diocese, there is a general permission given to priests to binate on weekdays and trinate on Sundays if there is pastoral need; I presume that a similar general permission is given in all the dioceses of England and Wales since there is very commonly a pastoral need.
§2. If there is a shortage of priests, the local ordinary can allow priests to celebrate twice a day for a just cause, or if pastoral necessity requires it, even three times on Sundays and holy days of obligation.
Therefore, the law on "bination" tends to be forgotten since permission is routinely given in accordance with canon 905.2. Suddenly now it is mentioned in connection with the celebration of Mass in the extraordinary form. I cannot see how it can be relevant except perhaps to remind priests that they should not say three Masses on a weekday or four on a Sunday. To binate in order to offer people the extraordinary form of Mass if they have asked for it seems to be a perfectly good pastoral reason. I do so myself, for example, when asked to celebrate the Missa Cantata at Maiden Lane. Having said my parish Mass in the morning, I am quite happy that it is a good pastoral reason to celebrate Mass if there is going to be a group of servers, a plainchant choir and a Church full of people.
Since we are on the question of bination, there is something that has been on my mind for quite a while. It is not uncommon for priests to attend a Mass for a particular occasion (blessing of the school computers, awarding of the bene merenti, you know the sort of thing). Although most priests will have said a parish weekday Mass earlier, it is usually presumed that they will concelebrate. I am increasingly uncomfortable about this. There is a good pastoral reason for a priest to attend the Mass but I cannot see that there is any pastoral reason for him to concelebrate, thereby offering Mass a second time in the day.
The priest should not simply attend as part of the congregation, however. Redemptionis Sacramentum addresses this matter:
128. Holy Mass and other liturgical celebrations, which are acts of Christ and of the people of God hierarchically constituted, are ordered in such a way that the sacred ministers and the lay faithful manifestly take part in them each according to his own condition. It is preferable therefore that “Priests who are present at a Eucharistic Celebration, unless excused for a good reason, should as a rule exercise the office proper to their Order and thus take part as concelebrants, wearing the sacred vestments. Otherwise, they wear their proper choir dress or a surplice over a cassock.” It is not fitting, except in rare and exceptional cases and with reasonable cause, for them to participate at Mass, as regards to externals, in the manner of the lay faithful.Sometimes it is urged that priests should sit in the congregation so that the celebration does not become "dominated" by clerical males. It is worth remembering the above section from Redemptionis Sacramentum kicks that nonsense firmly into touch.
Some priests might argue that Deanery or other similar Masses have something of the character of "conventual Masses" where it is explicitly permitted for a priest to concelebrate even though he has said a Mass for the faithful earlier in the day. I would not want to criticise anyone who took this view but it seems to be a perfectly sensible reading of canon law and liturgical law for the priest who has already said Mass to choose to attend "in choir", that is, wearing a cassock and cotta and not concelebrating.
Fr Thomas Kocik wrote a good article on this subject for Antiphon Magazine (10.2 2006) entitled Preaching through the Choir: The Merits of Assisting at Mass In choro (pdf 105kb)