Every time a team signs a free agent, it has a chance to improve its roster for the upcoming season. Every time a team signs a free agent away from a division foe, it has a chance to improve its roster while also weakening a direct competitor.

In that way, an impact player hitting the open market and then changing teams within the same division can be something of a double whammy.

• Hot Stove Tracker

These sorts of moves don’t always work out, to be sure. (See Arizona’s acquisition of Madison Bumgarner last winter, for example). Still, they make for intriguing possibilities.

So as we wait for the Hot Stove to kick into high gear, here is one team from each division that could snatch a notable free agent away from a rival this offseason.

AMERICAN LEAGUE EAST

Blue Jays sign INF DJ LeMahieu away from Yankees

While it’s still widely assumed that New York will do what it takes to retain LeMahieu, no other team has been connected more to the 2020 AL batting champion in offseason rumors than Toronto. It would make quite a statement for the up-and-coming Blue Jays to go out and land the 32-year-old, given how infrequently the Yanks tend to lose bidding wars. And the idea certainly is tempting. While LeMahieu has primarily played second base in his career, he also has corner-infield experience and could slide in at either first or third with Toronto, depending on the club’s plans for Vladimir Guerrero Jr. But this move would first and foremost be about LeMahieu’s bat, which produced a .336/.386/.536 line as a Yankee and would do wonders for the Blue Jays’ hopes of jumping past the Yankees and Rays in 2021.

One more to watch: Blue Jays sign CF Jackie Bradley Jr. away from Red Sox

AL CENTRAL

White Sox sign DH Nelson Cruz away from Twins

Like LeMahieu, Cruz almost seems destined to re-sign with his 2020 team. Not only has the 40-year-old slugger been as productive as ever in Minnesota, but he appeared to fit in perfectly there. Still, his free agency presents a major opportunity for the White Sox, who came within one game of unseating the Twins as division champs this year. Right-handed power is not exactly a glaring need for a club that employs José Abreu, Eloy Jiménez and Luis Robert, among others, and the White Sox have more use for pitching (perhaps even Twins free agent Jake Odorizzi). But adding to a strength can be a worthy endeavor, too. Just take a moment to envision the Chicago lineup with the Boomstick in the middle and you will understand why the club might pursue it.

One more to watch: Indians sign LF Eddie Rosario away from Twins

AL WEST

Angels sign RP Liam Hendriks away from A’s

Luring free-agent shortstop Marcus Semien away from Oakland would have been the best fit here, but that was before the Angels traded for José Iglesias on Wednesday. The Halos still need lots of help in both the rotation and bullpen, however. While spreading their free-agent dollars around to multiple relief arms could be the savvier course of action for new general manager Perry Minasian, there’s also something to be said for landing the best player available. At this position, that’s Hendriks. After saving 39 games with a 1.79 ERA and 13.1 K/9 rate over the past two seasons in Oakland, Hendriks would step right into the closer's role in Los Angeles and help a team that tied for the most blown saves in MLB in 2020 (14).

One more to watch: Rangers sign OF George Springer away from Astros

NATIONAL LEAGUE EAST

Mets sign C J.T. Realmuto away from Phillies

What else were you expecting here? This has probably been the most discussed free-agent rumor of this offseason, and for good reason. The Mets need a catcher, new owner Steve Cohen seems determined to make a splash right away and Realmuto is arguably the best player available on the open market. It seems like an ideal match, but those don’t always translate from paper to real life. The Mets could spend their money on Trevor Bauer or George Springer instead -- perhaps settling for James McCann behind the plate -- and Realmuto himself will have other motivated suitors. With that said, there might not be a move that announces Cohen’s presence with more authority than robbing an NL East opponent of MLB’s top all-around catcher.

One more to watch: Nationals sign LF Marcell Ozuna away from Braves

NL CENTRAL

Cardinals sign LF Kyle Schwarber away from Cubs

The Cubs non-tendered Schwarber on Wednesday, as the club looks to cut payroll. Their loss could be the Cardinals’ gain. While Schwarber is a one-dimensional player at this point, that one dimension (power from the left side of the plate) can be pretty impressive. Schwarber has homered once per 13.4 at-bats against righties in his career, MLB’s fifth-best ratio since 2015 (minimum 1,000 at-bats vs. RHP). The power-starved Cardinals absolutely could use that sort of big bat in their lineup, although the fit may depend, in part, on whether the universal DH remains in place for 2021. If Schwarber does switch sides in one of baseball’s best rivalries, it could make his departure sting all the more for Chicago fans.

One more to watch: Cubs sign 2B Kolten Wong away from Cardinals

NL WEST

Giants sign OF David Dahl away from Rockies

Dahl was one of the most surprising non-tenders at Wednesday’s deadline, given that the 26-year-old -- the 10th overall pick in the 2012 MLB Draft and a ‘19 All-Star -- has been a pretty productive hitter when healthy. Of course, he hasn’t been healthy often and struggled in limited action this past season. Playing half of your games at Coors Field can be a blessing but also a curse, and hitters can absolutely thrive after leaving. (Look no further than LeMahieu). It may be well worth it for the Giants to take a low-risk shot at seeing what Dahl has to offer their rebuilding efforts, at least as a center-field platoon partner for Mauricio Dubón. If he can finally reach his potential in San Francisco, it would mean quite a bit of regret for Colorado.

One more to watch: Giants sign RHP Garrett Richards away from Padres