How do Catholics explain 1 Corinthians 11:21 in light of Transubstantiation? Catholicism interprets 1 Corinthians 11:17-34 in light of the dogma of transubstantiation ( = the miracle of bread changing into Jesus' real flesh and wine changing into Jesus' real blood performed by a Catholic priest in the person of Jesus Christ). (source)


  "For every one taketh before his own supper to eat. And one indeed is
  hungry and another is drunk."
  
  1 Corinthians 11:21 (Douay-Rheims)


Does this show that in Catholicism, it is possible to get drunk with the real blood of Jesus Christ, to be intoxicated with him?
The bread and wine we offer at Mass do become, in Catholic understanding, "truly, really, and substantially, the body and blood together with the soul and divinity of our Lord Jesus Christ"1, and this is what we consume in the Eucharist.

However, this does not mean&mdash;as I mentioned in this answer&mdash;that the sacrificial offerings are no longer like the originals in any way. As the term "transubstantiation" should indicate, what is changed in the process is the substance, in the older philosophical sense of "that which makes something to be what it is". The accidents, that is, "those things which happen to be properties of an object", do not change.

In particular, that means that one can measure alcoholic content (an accident of the wine) even after transubstantiation; and thus, at least in theory, it would be possible to become drunk from it. Deliberately doing so, of course, would be a gross impertinence to Our Lord. Canon law provides for an excommunication in this or a similar case:


  Canon 1367. A person who throws away the consecrated species or takes or retains them for a sacrilegious purpose2 incurs a latae sententiae excommunication reserved to the Apostolic See; moreover, a cleric can be punished with another penalty, not excluding dismissal from the clerical state.


(emphasis added)



1(Council of Trent, XIIIth session, Canon I)
2Certainly the purpose of becoming drunk off the species of wine would be "a sacrilegious purpose".