BOSTON -- Another relief pitcher or a third baseman?

After a series-opening 4-3 loss to the Toronto Blue Jays on Monday night -- exactly two weeks before the non-waiver trade deadline -- it became clear yet again that the Boston Red Sox need to address not one, but both of those positions.

Save for a six-batter belch that produced three runs in the seventh inning, the Sox were shut down by Blue Jays starter Marcus Stroman, hardly alone in his mastery of an offense that has scored all of 26 runs in the past 10 games.

And after the game was tied and Mookie Betts got thrown out at home plate trying to score from first base on a double, the Jays needed only four batters to take back the lead in the top of the eighth inning against reliever Heath Hembree -- the second-most reliable healthy setup option for manager John Farrell.

The whole thing surely compelled Red Sox president of baseball operations Dave Dombrowski to give his phone a strenuous postgame workout.

But after nearly two years of trading several top prospects -- outfielder Manuel Margot for Craig Kimbrel, right-hander Anderson Espinoza for Drew Pomeranz, infielder Mauricio Dubon for Tyler Thornburg and infielder Yoan Moncada and flame-throwing Michael Kopech for Chris Sale -- Dombrowski doesn't appear inclined to weaken the Red Sox's farm system any further.

"I don't see them shipping off top-tier guys," a major league source with knowledge of the Red Sox's thinking said Monday, presumably referring to Triple-A third baseman Rafael Devers and 18-year-old lefty Jason Groome.

Here's the thing: They might not have to.

Todd Frazier will be a free agent at season's end, so the Chicago White Sox can't expect to get back more than a fringe prospect, even if they help subsidize the nearly $6 million Frazier is owed this year. And while trading for Frazier won't guarantee the Red Sox the American League pennant -- he's batting .207 with a .712 OPS and typically is a better hitter before the All-Star break -- he would still represent an upgrade at a position where Boston has used eight players and produced a league-worst .610 OPS.

Frazier would also bring home run power to an offense that's sorely lacking in that area. Since the beginning of June, he has nine homers, which is more than any Red Sox player during that span, and is slugging .508, better than every Red Sox hitter except Jackie Bradley Jr. (.519).

Farrell can talk all he wants about shuffling the batting order to generate more offense, a possibility he mentioned after Monday night's game. But the reality is that the Red Sox have been short at least one run-producer for most of the season, forcing them to rely on stringing together hits to score runs.

Lately, it has been an arduous chore. In the past 10 games, the Sox are 7-for-70 with runners in scoring position. Frazier, who has 16 homers and hit 40 only a year ago, would at least offer another power threat.

The White Sox's best chance for any real return for Frazier would be to package him with a reliever, and they have several to choose from, including setup men Tommy Kahnle (2.50 ERA, 15 strikeouts per nine innings) and Anthony Swarzak (2.47 ERA, 9.9 K/9), and closer David Robertson (2.70 ERA, 12.7 K/9). During the trade talks for Sale in December, the White Sox thought about expanding the deal by including a reliever, but decided to focus on getting the most they could for their best player. It wouldn't be a surprise if they try to sell the Red Sox on one of their relievers now.

But there are other relief options, too. Philadelphia Phillies right-hander Pat Neshek, for instance, will be a free agent at the end of the season, and like Frazier, probably won't command a big return. He would slot into the eighth inning, pushing Matt Barnes and Joe Kelly into the seventh.

History tells us Dombrowski won't stand pat at the deadline. He isn't known as Dealin' Dave for nothing. And since they returned from the All-Star break, the Red Sox's flaws have been on full display, never more so than Monday night.