The Catena Aurea says of the tabernacles in this passage:
Origenes: Hereupon follows what the warm Peter spake, "Peter answered and said unto Jesus, Lord, it is good for us to be here." Because he had heard that He must go up to Jerusalem, he yet fears for Christ; but after his rebuke he dares not again say, "Be propitious to thyself, Lord," but suggests the same covertly under other guise. For seeing in this place great quietness and solitude, he thought that this would be a fit place to take up their abode in, saying, "Lord, it is good for us to be here." And he sought to remain here ever, therefore he proposes the tabernacles, "If thou wilt, let us make here three tabernacles." For he concluded if he should do this, Christ would not go up to Jerusalem, and if He should not go up to Jerusalem, He should not die, for he knew that there the Scribes laid wait for Him.
Remigius: Otherwise; At this view of the majesty of the Lord, and His two servants, Peter was so delighted, that, forgetting every thing else in the world, he would abide here for ever. But if Peter was then so fired with admiration, what ravishment will it not be to behold the King in His proper beauty, and to mingle in the choir of the Angels, and of all the saints? In that Peter says, "Lord, if thou wilt," he shews the submission of a dutiful and obedient servant.
Jerome: Yet art thou wrong, Peter, and as another Evangelist saysLuke 9:33, knowest not what thou sayest. Think not of three tabernacles, when there is but one tabernacle of the Gospel in which both Law and Prophets are to be repeated. But if thou wilt have three tabernacles, set not the servants equal with their Lord, but make three tabernacles, yea make one for the Father, Son, and Holy Spirit, that They whose divinity is one, may have but one tabernacle, in thy bosom.
The commentators here link the three tents were meant as a ploy to dissuade the Lord from going to His Passion, as he knew that He would. In this sense, Peter would follow protocol and set up a separate tent for each VIP — it would be rude of them to make them share a tent, and they might have refused and gone off, prompting Jesus to go down from the Mount.
St. Jerome, of course, remembers to rebuke St. Peter in his commentary regarding the very point of placing Jesus in the same level as Moses and Elijah. If there will be three tents, it should be one for each person of the Trinity. However, he implies that St. Peter wasn't trying to make a theological statement with his three tabernacles, but it ends up suggesting one in the mind of the Gospel readers.