Houston Astros: Ryne Stanek
Ryne Stanek has spent each of the last three seasons with the Astros and has been an important piece to what is always a strong bullpen. He's made at least 55 appearances in each of the last three seasons for Houston and has 20 postseason appearances to his ledger as well.
The right-hander had a bit of a down year in 2023, posting a 4.09 ERA in 50.2 innings pitched, but he had 51 strikeouts and his 9.9% walk rate was his best since 2018 with Tampa Bay. Obviously he has work to do to get close to the 1.15 ERA he had in 59 2022 appearances, but the Angels wouldn't expect him to come close to that anyway.
Like Fujinami, the Angels wouldn't be signing Stanek to close, but he'd add a ton of experience to a bullpen that needs it and can be productive in the sixth or seventh innings. He's familiar with the AL West, has a long track record of success, and his 2.08 postseason ERA is extremely attractive.
Adding the 32-year-old for a year or two to this bullpen would absolutely make it better, and would also add a much-needed veteran presence.