SAN DIEGO — A quiet winter meetings for the Red Sox became busy late, as the team added three players – infielders Jonathan Arauz and Jose Peraza and starter Martin Perez – before departing San Diego on Thursday. All three additions filled clear holes on Boston’s roster, with Arauz and Peraza entering a wide-open second base competition and Perez replacing the departed Rick Porcello as the fifth starter.

The prevailing thought entering the meetings was that new chief baseball officer Chaim Bloom would be handcuffed by the team’s goal of cutting payroll, and, as a result, have to subtract to the roster before adding. He downplayed that idea during his meeting with reporters on Day 1 in San Diego, foreshadowing how he’d spend the rest of his week at the Manchester Grand Hyatt hotel.

“I think certain acquisitions fit a narrower niche than others do,” Bloom said. “But I think it’s really more about trying to assess the whole landscape, trying to make sure we are active enough to understand the opportunities are available to us and react accordingly. That doesn’t necessarily mean the dominoes have to fall in a certain sequence. We just need to make sure we are doing things in an order that ultimately makes sense.”

In essence, Bloom was saying he was willing to make Boston’s payroll problem worse before working to make it better. If someone – like Peraza or Perez – was a good fit for the roster and was ready to sign this early in the offseason, the Red Sox were going to get deals done even if it meant the projected payroll would continue to skyrocket past their $208 million goal.

That never meant the Sox would ever be in on top free agents like Gerrit Cole or Stephen Strasburg, but it did allow the signings of Peraza and Perez to come together fairly quickly. Peraza, a versatile 25-year-old who projects to play mostly second base next season, was signed to a one-year deal in the $3 million range. Perez, whose advanced metrics paint a different picture of his 2019 season than his traditional numbers, got $6 million with a $6.25 million club option for 2021.

Suddenly, the Sox have their replacements for both Rick Porcello and Brock Holt at cheaper costs than it would have taken to retain both fan favorites. The second base picture is a murky one, with Peraza, Arauz, Marco Hernandez, Tzu-Wei Lin, Michael Chavis and maybe even Dustin Pedroia in the mix, but the Sox have a ton of different options to learn more about in spring training. As of now, Perez will be in the rotation, behind Chris Sale, David Price, Eduardo Rodriguez and Nathan Eovaldi unless one of those four is traded.

Boston now has just a few clear needs on the roster: a backup catcher, a first baseman and – if the price is right – a bullpen addition or two. There are some internal options at first (Josh Ockimey? Bobby Dalbec?) and in the bullpen (Tanner Houck? Travis Lakins? Colten Brewer?) and a few minor-league signees that will likely be in the mix come spring, while the organization is looking outside to find Christian Vazquez’s backup behind the plate.

Instead of subtracting before adding, it’s clear Bloom is looking to do both simultaneously. While the Sox were finalizing their deals with Peraza and Perez, they were working hard to trade left-hander Price, who is reportedly drawing interest from multiple clubs (including the Cardinals, Angels, Padres and others) and are likely still considering the possibility of moving outfielder Jackie Bradley Jr.

The latest payroll projection has the Sox at over $231 million for next season, nearly $23.25 million over the $208 million mark. It’s clear Boston still intends to get there before the beginning of spring training, making a trade of someone like Price (owed $31 million), Eovaldi ($17 million), Bradley Jr. (projected at $11 million) or Mookie Betts (projected at $27.7 million) likely, if not inevitable.

Though the overriding theme of this winter is subtraction, the additions are notable too. Some tweaks could fully unlock Peraza, who the Red Sox like for his versatility and athleticism, and Perez is due to be more lucky than he was in 2019. The Red Sox could still contend in 2020 by keeping almost the entire core together, tweaking a few spots on the outskirts of the roster to save money and having some internal options step up to replace the production of a high-priced player who is traded.

Here are some other final thoughts from the meetings:

• Price, not Betts, looks like the key piece most likely to be traded.

Entering the meetings, the consensus choice for the Red Sox was to trade Betts, who is projected to earn $27.7 million in 2020 and has not done anything to prove he’s serious about signing a long-term deal in Boston. By the end of the festivities, it was clear Price is more likely to be moved.

Previously, the prevailing thought was that Price – due $96 million over three years, entering his age-34 season and coming off a year in which he missed significant time due to injury – would not be attractive to other clubs. But the market has developed in Boston’s favor, with teams that lost out on Cole and Strasburg forced to look at the trade market considering the lackluster options still available in free agency.

A handful of mediocre teams from 2019 (like the Angels, White Sox and Padres) are being aggressive early in the winter in a clear sign of going all-in for 2020. Teams in that position sometimes have to take big risks, and Price would certainly qualify.

It remains to be seen exactly how the Sox would frame a Price deal and whether or not they’d have to attach a promising young player or eat some of Price’s money to do so. But it’s clear they’re looking to trade him and beginning to look like Betts will stay put as a result.

• Infield picture beginning to take shape

The two sides of the Sox’s infield – a left side with stars Rafael Devers and Xander Bogaerts entrenched for years to come and a right side with a bunch of unproven options and question marks – could not be more different in terms of how the front office must approach them this winter. With Mitch Moreland and Brock Holt likely signing elsewhere, Steve Pearce retiring and Pedroia unlikely to ever play again, the Sox entered the offseason with a mix of top prospects (like Dalbec and Chavis) and utility players (Hernandez and Lin) as their options at first and second base.

That picture became even more crowded Thursday when the Sox added Arauz (a 21-year-old from the Astros’ organization who profiles as a utility player) and Peraza (a 25-year-old with offensive potential who can play a variety of positions) within a couple hours. Both should factor into the competition for playing time during spring training and come as low-risk, cheap options.

The moves also almost certainly signal the end of Holt’s tenure in Boston. He seems likely to receive a significant contract elsewhere.

• Road to division title gets tougher with Cole signing

The Yankees made the biggest splash of the entire winter, signing Cole to a nine-year, $324 million contract. After a few years of building their core from the inside, the Yanks reverted back to the old versions of themselves and simply outspent everyone else to land one of the best pitchers in baseball.

New York was markedly better than Boston in 2019, winning 19 more games than Boston and winning 14 of the 19 head-to-head matchups between the clubs. The Cole signing, at least on paper, furthers the gap between the Yankees and Sox.