The thought, "there shall be many" will be concluded in verse 3, and will be discussed there.
The day of the Lord's "marvelous work" will be when He "remembers [His] covenants" made previously to "the children of men." Those covenants to "the children of men" are all inclusive. This will include promises made to all mankind, without regard to their status as Israel, gentile, heathen, or even if they are living or dead as the work begins. It is the Lord's covenants made in the pre-earth councils, and is for all mankind.
As fulfillment of these complete covenants, the Lord will "set [His] hand again the second time to recover my people." Now the focus moves from "the children of men" to a sub-set of those He calls "my people." His people are, by definition, necessarily affiliated with "the house of Israel" through covenant. These would include those called the "remnant" as well as those believing "gentiles" who accept the covenant and return through repentance to Christ.
Why do we see layers of covenants or promises referred to here? Why the covenants made "unto the children of men?" Why then further "the house of Israel?" Why further "promises made unto Nephi?" Why still further "thy father" [meaning Lehi]? Why a work which will affect all these groups? And, finally, why does all of the foregoing return to "remembering Nephi's seed?" What role does Nephi's seed, or remnant fulfill in the promises made to all mankind?
Why does the Lord make a covenant with all humanity, but then reiterate the covenant with Abraham? Why do the covenants get repeated through Isaac and Jacob, the last of whom supplies the name of the covenant people "Israel?" Why, after all those covenant recipients do the covenants get renewed with Lehi? Why immediately following Nephi do the covenants get renewed yet again in Nephi? Why does the Lord engage in this covenant making process to tie together the events of history and the lives of men? Can He still do this today? Does He still expect or want to enter into covenants with men today to further His purposes? Do those covenants necessarily get confined to an institution or priestly process rather than through Him, directly? Why not?
When we get to Nephi's descendants, why are they the ones who are to provide "a standard unto my people, which are of the house of Israel?" What does this say about the significance of the Book of Mormon? Why is it the "standard unto the Lord's people?" What does that do to clarify the condemnation resting upon the church under D&C 84: 57? How important is "the standard" established by the Lord? Why would Joseph Smith say the "fullness of the gospel" is contained in the Book of Mormon?
Why does the title page of the Book of Mormon, which was part of the translated record, contain this description: "Which is to show unto the remnant of the House of Israel what great things the Lord hath done for their fathers; and that they may know the covenants of the Lord, that they are not cast off forever—And also to the convincing of the Jew and Gentile that Jesus is the Christ, the Eternal God, manifesting himself unto all nations."
What does it mean that these words shall "hiss forth to the ends of the earth?"
Did you notice the Lord taking personal credit for the words of the Book of Mormon? What does the phrase "the words of your seed should proceed forth out of my mouth unto your seed; and my words shall hiss forth unto the ends of the earth?" How does the Lord taking personal credit for these words affect the Book of Mormon's significance?