This is an old outline I made of Romans 9-11 but I think it still will match decently with what I could find in an updated analysis
Address Problem of Ill Will Toward Jews. Proving God's faithfulness ( ch 9 to11)
Paul had to show God's faithfulness to Israel so that the gentiles would have a benevolent attitude toward Jews and that the Jews could be saved, as was one of the goals of Paul's ministry to gentiles. The additional goal was that the Roman gentiles had to be secure in God's faithfulness as it pertained to them
Address Problem of Ill Will Toward Jews. Proving God's faithfulness ( ch 9 to11)
A. Foundational information
i. Need and "right" for Israelites to enjoy promises (9:1-5)
ii. Narrowing of Israel to only bloodline who are also of promise (9:6-21)
a. Only a certain path was under promise under Abraham (9:6-13)
b. Argument for God's right to narrow the seed (9:14-19)
c. Problem of us questioning God's selection among Jews (9:20-21)
iii. God's patience prevented earlier time of wrath (9:22-24)
iv. Prophecies of people upon whom God would show mercy (9:25-29)
v. Failure of Israelites to come to Christ was not God's failure
a. Failure in their effort to follow law to get to righteousness (9:30-33)
b. Israel(bloodline) effort was to try to make their own righteousness(10:1-12)
・ Their effort was not without zeal (10:2)
・ They were ignorant of God's righteousness (10:3)
・ If they followed God, they would have come to Christ (10:4)
・ Trapping of righteousness by Law (10:5-7)
・ Word of righteousness by faith is near (10:8)
c. Nearness of faith was there for Israel (10:8-13)
・ It was now close by confessing Jesus (10:9)
・ It was a matter of the heart (10:10)
d. God's faithfulness to bring the message (10:14-17)
・ Since gospel has to go out (10:14-15)
・ But it was prophesied all would not accept the gospel (10:16)
・ But Israel heard (10:18)
・ Israelites should have known through prophecy of jealousy (10:19-20)
e. Apparent bleakness of situation (10:21)
B. Argument to Accept Jews
i. Situation isn't so bleak. God didn't cast off His people (11:1-7)
a. His people were in that present remnant (11:2-5)
b. It was a remnant by election of grace (11:6)
ii. Non-elect were hardened so Gospel would go to Gentiles (10:19,20 and 11:8-16)
a. Hardening prophesied (11:7-10)
b. Hardening to produce jealousy (11:11)
c. Expectation of Roman believers to have mercy (11:12-16)
C. Argument regarding Gentiles' boasting against Jews
i. Introduce Olive tree analogy, loosely about people of God (11:17-19)
ii. Be fearful instead of boastful (11:20-22)
iii. Still was opportunity for some to be found in remnant (11:23-24)
iv. Conclusion of Olive Branch analogy (11:25)
D. Conclusion of Paul's full argument
i. Re-emphasis that Israel (as the remnant) would be saved (11:26)
ii. God's faithfulness in accomplishing the prophecies (11:26-29)
iii. God's equal benefit to Gentiles and Jews (11:30-32)
E. Praise to God for His Plan and Wisdom (11:33-36)
Paul had to show God's faithfulness to Israel so that the gentiles would have a benevolent attitude toward Jews and that the Jews could be saved, as was one of the goals of Paul's ministry to gentiles. The additional goal was that the Roman gentiles had to be secure in God's faithfulness as it pertained to them