I have attempted to sketch a background in liturgical theology for what we call concelebration; although I must emphasise the word concelebration is a fairly modern term. What I have tried to do is to draw out of the rich and ancient texts and rituals of the Roman Liturgy the implications of those rites. And what we have found over and over again is the sense of the presbyterium as a corporate body; which acts corporately with its head, the Bishop.
This gives us our first helpful line on Eucharistic Concelebration. It is at its most natural when the presbyterium of a particular church gathers round its bishop for the celebration, with God's people, as a unity, of the Eucharistic Sacrifice. So Ordinations, Maundy Thursday, and perhaps in the context of a small mediterranean-style polis, the Easter Vigil, are occasions par excellence for this practice. One thinks also of Synods and the like). Vatican II encouraged this approach.
We of the Anglican Patrimony do well to remember the perception of our own Eric Mascall, that Concelebration, just like Private Masses, is based on the notion that a priest, when at the Eucharist, behaves most appropriately when he is discharging his liturgical role as priest. Writing at a time when Concelebration was known better in the Byzantine Tradition and the Private Masses were still common among Latin Catholics, Dr Mascall expressed the view that each of these practices seemed theologically closer to each other than either did to the 'middle-of-the-road' Anglican assumption that a priest, whenever possible, ought to mascarade as a layman when at the Eucharist.
But we are now far enough from the reintroduction of Concelebration into Western Catholicism to be able to have a fresh look at it. One recalls the observation of an oriental hierarch, viewing one of the big concelebrations of the new Western era, observing that 'When these Westerners get a new idea, they always carry it to extremes'. And, more divertingly, there is the reported phenomenon in Liberal American Catholicism of Concelebration being regarded as Politically Incorrect because it sets up a great male phalanx in opposition to the sensitive feminists at the other end of the church building.
That, of course, doesn't worry me. Those ladies are just going to get used to great waves of testosterone wafting down churches.