Bear ICOR 11:21 and the surrounding verses in mind. Paul is expressing outrage or at least concern over the way at what purports to be but fails to be "the Lord's supper" each one eats his own food, so one is hungry and another drunk. AND then AFTER the verse you cite, Paul appears to sum up with a solution to the courtesy and inequity problem: namely wait for one another and don't use this meal to satisfy hunger.
Consequently, the argument goes, (advocatus diaboli here) "discerning the body" just means discerning that the congregation is united as members of one body in Christ and so one's comportment at the mass should show that one sees that.
The Christians at or about the time of the Church's only Sacrifice and their communicating thereof, kept great feasts: which continued long, for that the relief of the poor upon the common charges of the richer sort, and the charity and unity of all sorts were much preserved thereby, for which cause they were called αγαπου, that is, Charities, of the ancient Fathers, and were kept commonly in Church houses or porches adjoining, or in the body of the Church (whereof see Tertullian Apolog. c. 19.; Clemens, Alexand.; St. Justin; St. Augustine cont. Faust. li. 20 c. 20.) after the Sacrifice and Communion was ended, as St. Chrysostom be. 27. in 1 Cor. in imitio judgeth.
Those feasts St. Paul here calleth Coenas Dominicas i.e. Lords Suppers, , because they were made in the Churches which then were called Dominica, that is, Our Lord's houses. The disorder there kept among the Corinthians in these Church feasts of charity, the Apostle seeketh here to redress, from the foul abuses expressed here in the text:
And as St. Ambrose in hunc locum (this place), and most good authors now think, this which he calleth Dominicam coenam, is not mean of the Blessed Sacrament,
as the circumstances also of the text do give, namely, the rejecting of the poor. The rich men's private devouring of all, not expecting one another, gluttony and drunkenness in the same, which cannot agree to the holy Sacrament.
And therefore the Heretics have small reason, upon this place, to name the said holy Sacrament, rather, the Supper of the Lord, than after the manner of the primitive Church, the Eucharist, MASS, or Liturgia. -Original and True Douay Reims Bible 1582
Ver. 20. The Lord's supper. So the apostle here calls the charity [Agape] feasts observed by the primitive Christians; and reprehends the abuses of the Corinthians on these occasions: which were the more criminal, because these feasts were accompanied with the celebrating the eucharistic sacrifice and sacrament. (Challoner) Haydock's Catholic Bible Commentary
This fits the context quite well, because later St Paul says they should prove themselves before drinking of the chalice, refering to the agape: Gonzo's Commentary, Free Republic Press, 2008
33 Wherefore, my brethren, when you come together to eat, wait for one another. 34 If any man be hungry, let him eat at home; that you come not together unto judgment. And the rest I will set in order, when I come.
What sayeth thou, Oh your Dawgness?
>> Consequently, the argument goes, (advocatus diaboli here) “discerning the body” just means discerning that the congregation is united as members of one body in Christ and so one’s comportment at the mass should show that one sees that. <<
A warning against gluttony at communion is certainly a key teaching in 1 Cor 11:34. That hardly suffices as the explanation for 11:27-33, though:
“Wherefore whosoever shall eat this bread, and drink [this] cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord. But let a man examine himself, and so let him eat of [that] bread, and drink of [that] cup. For he that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord’s body. For this cause many [are] weak and sickly among you, and many sleep. For if we would judge ourselves, we are not judged. But when we are judged, we are chastened of the Lord, that we should not be condemned with the world.”