navi prophets - Were there multiple Isaiahs?

Modern scholarship recognizes multiple authors of the book of Isaiah. While Isaiah 1-39 is attributed to the pre-exilic Isaiah ben Ammoz, Isaiah 40-66 is attributed to one or more later prophets writing at a later time. This view holds that Isaiah is a composite work, gathered together into one book under the presumption of single authorship. Evidence for multiple authorship is taken from dating parts of the book of Isaiah to time periods during the reigns of four Kings of Judah (starting with Uzziah), during the Babylonian captivity, and after the release of the exiles by Cyrus. This span is taken to be longer than the average human lifespan at this time.

My question is twofold:

1) Have the sages commented on the authorship of the book of Isaiah?

2) If multiple authors are recognized, why are their writings kept together in one book?

Answer

To answer the first part of your question, yes the sages discussed the authorship of Isaiah, and he did not write his own book.

See here Bava Bathra 15a

Hezekiah and his colleagues wrote (Mnemonic YMSHK) Isaiah,  Proverbs, the Song of Songs and Ecclesiastes.

Rashi explains that the prophets would write their prophecies at the end of their lives and since Isaiah was murdered by Menasheh as seen in the talmud here, folio b, Isaiah did not have a chance to write his own book.

As an additional point. Do we assume that that changes were made until the book was written and 'sealed'. No, not necessarily. Is it possible? Sure. Just a few lines earlier in Bava Bathra, at the bottom of 14b we are told

David wrote the Book of Psalms, including in it the work of the elders, namely, Adam, Melchizedek, Abraham, Moses, Heman, Yeduthun, Asaph, and the three sons of Korah

So even though David put the final touches on psalms, there were many authors. But we do see that whoever we accredit with writing it, got to put in what they chose to. (whether that itself was guided by prophecy seems irrelevant) So it would be possible that Hezekiah and his colleagues put content into the book we call Isaiah.

Of interest is the opinion of the Netziv in his commentary to the Song of Songs where he writes that these final authors actually made changes to the earlier prophetic words. He says the Moses version of psalm 90 read 'the days of man are 120 years'. David switched it to say 70. This pliability was only until the books were formally written down. He however does not point to Isaiah as part of his discussion.

Edit: We find in Vayikra Rabba 6:5(6) that a different prophet's short two passage prophecy, which was deemed too short to have it's own book, was in fact interpolated into Isiah's. These are the verses beginning with vs 19 in chapter 8.

אמר רבי סימון: בארי לא נתנבא אלא שני פסוקים ולא היה בהם כדי ספר ונטפלו בישעיה, ואלו הן: וכי יאמרו אליכם וחברו.

As mentioned in the comments by @mevaqesh there are some secretive comments made by Ibn Ezra alluding to a later authorship of chapters 40 and on. His comments are found in 40:1, 49:7 & 53:12. You can see a blog discussing that here. Of particular note is the ending comment there:

Note that Ibn Ezra wasn't motivated to come to his conclusion for any of the heretical reasons of the Modern Bible critics. Ibn Ezra obviously has no problem with a novi (prophet) seeing into the future, which is why he doesn't mention his ''secret'' in his peirush (explanation) either of the two places where Koresh's name is mentioned, which were the favorite proofs of the kofrim (heretics). Ibn Ezra came to his conclusions not because of any doubts as to the powers of nevuoh (prophecy), but rather as result of his sophisticated literary and grammatical sensibilities, his acute sensitivity to all the dimensions of what we call poshut pshat (simple understanding of the verse).

In other words, these premises are built on the fact that no mortal man could have mentioned an event before it happened. So therefore any post exile account must have been written by someone who lived post exile. However, we who believe in prophecy, as we must according to any Jewish authority, think this argument falls short. Any reason we would believe who the author is will have nothing to do with these arguments.