Even with the San Diego Padres having one of the best bullpens in all of baseball, the front office is still looking to make some additions before the trade deadline this year.San Diego has seen the team be able to stay afloat in the standings on the backs of a strong bullpen, but the front office wants to make sure that nobody is overworked.Star closer Mason Miller has already discussed how his heavy workload has impacted him recently, and this could lead the team to make some moves.In fact, Padres insider Dennis Lin of The Athletic has listed a few names that the team could go after. This includes two All-Star closers that would completely bolster this bullpen to help turn San Diego into a legitimate World Series threat."Still, more than two months before the Aug. 3 trade deadline, the Padres are exploring the market for relief help, league sources toldThe Athletic," Lin wrote."Relief is generally cheaper to acquire than, say, a mid-rotation arm. Potentially available names this summer include a pair of possible Hall of Fame closers: the Boston Red Sox’s Aroldis Chapman and Hader, now with the Houston Astros."Case For Padres To Go After Aroldis Chapman or Josh HaderWhen looking at both Chapman and Hader, either player could be the perfect addition to this bullpen unit. San Diego has a history with Hader, with him pitching for the team for a year and a half before he joined Houston in free agency.For the year, Hader has yet to make his debut for the Astros due to biceps tendonitis. But he did start his first rehab assignment in early May and should be making his season debut soon. Last season, Hader registered an ERA of 2.05, recording 28 saves in 29 opportunities. Hader is 32 years old, and he could offer the Padres more long-term answers in the bullpen as he's under contract for multiple seasons.A back of the bullpen that includes Hader and Miller would be downright unfair.As for Chapman, he has once again reminded everyone around baseball why he remains a top arm, despite his age (38). Overall, Chapman has appeared in 18 games for the Red Sox, posting an ERA of 0.51 while recording 12 saves in 12 opportunities. Chapman has continued his excellent tenure with the Red Sox, and with Boston struggling this year, he could be moved. In 2025, the left-hander put up an ERA of 1.17 with 32 saves.Both Chapman and Hader could help ease the workload of multiple guys in the Padres' bullpen. And both stars have been excellent this season, but the decision to go after one of them could come down to finances and what San Diego has to trade.Chapman is the older player of the two closers, with him having a conditional mutual option for $13 million for the 2027 season. Hader, on the other hand, has two more seasons on his contract, with him being scheduled to make $19 million each year.So, if the Padres want to shore up the bullpen for the next couple of years, Hader makes more sense. But if the team is worried about cutting salary or not taking on more long-term money, Chapman should be the target.Overall, the Padres can't go wrong by going after either of these two star relief pitchers. And if the front office can make another splash move like this, the sky really is the limit for this organization this season.Sign up for our free newsletter and follow us on Facebook and X/Twitter for the latest newsAdd us as a preferred source on GoogleFollow