NASHVILLE — Over the last three days, as baseball people began to assemble for the annual Winter Meetings, we found that scouts and executives were willing to help Dave Dombrowski with a few ideas on how he could improve the Red Sox, even beyond the spectacular start to his Red Sox career.

We asked them to consider . . .

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 The Red Sox need a No. 2 or No. 3 starter;

 The Sox may want to trade one of their eight starting pitchers (after David Price);

 The Sox would like to find a new home for Hanley Ramirez;

 The Sox probably need to focus on the middle of the order for this year and certainly beyond when David Ortiz retires.

With those goals in mind, here are some of the suggestions from our sources:

1. Angels I — Clay Buchholz, Joe Kelly, Pablo Sandoval, and Brock Holt for Garrett Richards. Comment: Probably far-fetched the Sox could get Richards.

2. Angels II — Holt, Deven Marrero, and Travis Shaw for Hector Santiago. Comment: Santiago gave up a league-high 29 homers. Probably not a good idea.

3. Orioles — Ramirez and half the contract ($33 million) for a couple of minor leaguers. Comment: Seems like a good landing place for Ramirez considering Orioles GM Dan Duquette signed him originally.

4. Astros — Shaw and Blake Swihart for Lance McCullers and a prospect. Comment: Tough to get McCullers, but precisely the type of young pitcher they would want.

5. A’s I — Swihart, Holt, Kelly, Andrew Benintendi, and Henry Owens for Sonny Gray. Comment: I would think Billy Beane has to think seriously about this one.

6. A’s II — Swihart, Owens, and Yoan Moncada for Gray. Comment: Beane would have to think even longer and harder about this one.

7. Mariners — Ramirez and half the salary for a player to be named. Comment: See comment on Orioles scenario.

8. Indians — Shaw and Owens (or Brian Johnson) for Carlos Carrasco. Comment: Doable. The Indians get their hitter and a younger pitcher.

9. White Sox I — Dustin Pedroia for Jose Quintana. Comment: Don’t think the Red Sox would trade their de facto captain, especially with Ortiz leaving after this year. But anything is possible.

10. White Sox II — Swihart, Kelly, Owens, and Rafael Devers for Chris Sale. Comment: Seems like a lot to give up, but we love Sale.

11. Braves — Swihart and Devers for Shelby Miller. Comment: Miller is precisely the type of pitcher the Red Sox would be looking for.

12. Cubs — Owens, Kelly (or Buchholz), and Jackie Bradley Jr. for Jorge Soler and a prospect. Comment: The Red Sox have to start thinking about young power, and Soler has it.

13. Padres I — Shaw for James Shields and the Padres pick up about $6 million a year on the remaining of contract. Comment: Shields didn’t have a great year, but it wasn’t a disaster.

14. Padres II — Shaw and Brian Johnson for Tyson Ross. Comment: I’ll pass on this one.

15. Rangers — Ramirez and cash for a player to be named. Comment: Sure, why not?

16. Reds – Owens, Holt, and a mid-level prospect for Todd Frazier. Comment: A few things would have to take place before Frazier comes to the Red Sox. For one, they’d have to move Ramirez and/or Sandoval to make room at first or third.

17. Sign Chris Davis — Comment: What a splash that would be. Davis can hit home runs and drive in lots of runs anywhere. I don’t care how many times he strikes out; 40 home runs and 110 RBIs make up for it.

18. Mets — Bradley, Owens, and Mookie Betts for Matt Harvey. Comment: Mets aren’t trading Harvey.

19. Tigers — Ramirez for Justin Verlander. Comment: Two bad contracts (Verlander has four more years at $28 million per year, plus a vesting option for a fifth year), but this one was already officially shot down by Dombrowski and Tigers GM Al Avila.

20. Royals — Buchholz for Luke Hochevar and a prospect. Comment: Looks like a good deal for Red Sox, bolstering their bullpen and adding protection for a worn-out Junichi Tazawa and comebacking Koji Uehara.

The Red Sox have talked to the Braves about Miller, who would be an ideal fit in Boston’s rotation. This acquisition would seem the most realistic of the pitching possibilities, but it will cost prospects that they probably don’t want to give up.

The Sox have made it clear they don’t want to deal Betts, Benintendi, Devers, Moncada, or Xander Bogaerts. But if it’s a Gray, Sale, or Harvey coming back in return, at what point do they give in on one or two of them? It all depends on how confident Dombrowski feels.

Eduardo Rodriguez may be that solid No. 2, but who knows if he gets better, stays stagnant, or declines in his sophomore season? They should keep the pressure off him for a while.

It’s hard to count on the oft-injured Buchholz to be a consistent. And while you think Rick Porcello can’t be worse than last year, how do you enter the season having to depend on him for a 15-win performance?

It appears that Shaw has garnered a lot of respect around the league, and his value is pretty high. If the Sox can’t move Sandoval and Ramirez, Shaw would end up as a platoon player, and that won’t be good for him.

It doesn’t appear the Sox will be in the market for some of the remaining free agent arms. Yovani Gallardo, Mike Leake, Wei-Yin Chen, and Scott Kazmir will all be pricey.

It’s nice that a lot of people would like to help Dombrowski.

Lots of ideas. Lots of ways to go if you’re Dombrowski.

Nick Cafardo can be reached at cafardo@globe.com.