Towards the end of his distinguished career —his moonlighting career, that is, his day job, was doorkeeper at Archbishop's House, Westminster, according to the late Brian Brindley—Archdale King (who really needs his own page on Wikipedia) wrote a book on concelebration. I read it several years ago, and it seemed to me that he had been asked to write an authoritative book justifying the practice. The result didn't seem to me to be very convincing, and I suspect that, whatever his official conclusions, he wasn't convinced either. His arguments worked by, effectively, blurring the distinction between true sacramental concelebration, ritual concelebration, and parallel Masses.
Ritual concelebration has a well established pedigree in the Church. This is when priests or bishops assist at Mass dressed in the eucharistic vestments of their order, but do not say the words of consecration with the celebrant. Most, if not all, of the Eastern rites use this form from time to time—there was a famous celebration at Vatican II which no doubt inspired the 'restoration' of the custom to the West. The Carthusians would 'concelebrate' in this fashion also, and I think that one might argue that the ceremonial at a papal coronation was another manifestation, where the cardinal bishops wear cope, the cardinal priests wear chasubles and the cardinal deacons wear dalmatics throughout the Mass.
Parallel Masses are rarer in the Church, but were popular in some places from the second world war until the Council. Chevetogne, the multi-ritual Benedictine/Basilian monastery in Belgium founded by that liturgical enthusiast, Dom Lambert Beaudouin, used this enthusiastically. A friend who visited in the late fifties or early sixties, was bemused to see, at low Mass time, a number of altars being wheeled out into the nave of the Latin church at which priests would celebrate Mass in synchrony, each keeping an eye on the celebrant at the high altar. Odd, I think.
Fr Hunwicke is quite right to insist that the Church has found that the concelebration at ordination in the Latin rite is a true, sacramental, celebration for each priest and for the bishop. It was always said that each ordinatus was entitled to take a stipend for his Mass, and that, for me, clinches it. But I honestly think that this is the only justification for the present day custom. One of the ordines romani has the cardinals celebrating Mass with the Holy Father, each with a kneeling acolyte holding a glass paten with a host for him to consecrate. My instinct is that this is not a true concelebration, rather a Chevetogne-style parallel Mass. I do not think that Archdale King managed to come up with any other precedent.
So, I think we cannot deny the liceity of concelebration, but it rests on very thin ground. I prefer really to think of it in terms of appropriateness. Modern liturgists are very keen that signs and symbols should be as patent or obvious as possible. The sign that fifty priests, all in persona Christi, give to the assembled faithful is surely not a good one if what we are trying to communicate is Christ breaking the Eucharistic bread for his people—or, as I would prefer to say, immolating himself for our salvation and sanctification in an unbloody fashion, using the forms he established at the Last Supper. One Christ, in other words, not many. And is it really valid (as I have asked before) if the celebrant cannot even see the altar, let alone the host?
There is the argument that the assemblage of celebrants shows forth the unity of the priesthood. Yes, I can see that, but it is a minor point, and could surely be established in other ways. But I would concede that if we must have concelebration, there are occasions when it is more appropriate than others. Perhaps at the Chrism Mass, for instance, or for all priests present at an ordination, and not solely the ordinati. And, I think, when a bishop visits a parish, it may well be appropriate and teaching for the parish clergy to concelebrate with him (provided the bishop is the 'chief celebrant') so that the people may see the proper relationship of bishop and priest, whose ministry depends on the successor to the apostles.