How Romans 9-11 fits into the overall scheme and purpose of the book of Romans

Romans 9-11, demonstrate to us an overall plan that God has set in place for the world’s salvation through his revelation of salvation history. The overall scheme seems to be the salvation-history. Now let’s look at the purpose. Paul demonstrates God’s desire to be revealed with all who will believe and confess that Jesus is the Christ and Jesus was raised from the dead. Even to the point of saving the gentiles to provoke Israel into repentance. These passages also reflect God’s faithfulness to Israel by fulfillment of his covenant promise to Israel. There has always been and will always be a remnant of believers to fulfill God’s promise in his faithfulness to his chosen people. This demonstrates God’s word will never be compromised, no matter how grim the circumstances may seem.
These passages can also be summed up as Paul clearing up may key theological issues. Paul develops his theology of predestination or Justification. However, I think the most important reason or purpose that Paul wrote this was to present the Gospel of Jesus Christ, while embracing his Jewish heritage and God keeping with the promises of the Old Testament.
I especially like how Douglas Moo sums this up by showing that Romans 9-11 is a celebration for God’s unshakable love to us and he reveals his plan to us all. He states,

“God’s wisdom and knowledge, his plans and his purposes, are ultimately quite
beyond the capacity of any human being figured out. In other words God is
sovereign and we must come to a point that we stop questioning God and
surrender and accept His will and bow down and worship our Creator."

Moo, Douglas J. Encountering The Book of Romans. Grand Rapids: Baker Academic, 2002.
Schreiner, Thomas R. Romans. Grand Rapids: Baker Acaddemic, 1998.