They may have found a suitable option in infielder Danny Valencia.
Toronto acquired Valencia — who's hitting .333 against left-handed pitchers in his career — from the Kansas City Royals on Monday in exchange for right-handed pitcher Liam Hendriks and catcher Erik Kratz.
"We have a lot of left-handed bats on the roster right now and we certainly could use some help from the right side" Blue Jays manager Alex Anthopoulos said on a conference call. "Danny's had a lot of success. We've actually inquired about him in the past but haven't been able to get anything done.
"We've been really trying to find all year ... that right-handed bat. He's had success at the big league level doing that and doing it well. It's a good fit for us."
Through 36 games with the Royals this season, Valencia has a .282 batting average — including a .354/.386/.492 slashline against lefties — with five doubles, two home runs and 11 RBIs.
He's expected to report Tuesday to Fenway Park in Boston, where the Jays are currently playing a three-game set.
Aside from a valuable bat, the 29-year-old Valencia is also versatile in the field, playing most of his career big league games at third base but also filling in at second and first, as well as the DH spot.
Anthopoulos said that flexibility was a big draw for the Blue Jays, who are still missing starting first baseman/designated hitters Edwin Encarnacion (strained quadriceps) and Adam Lind (foot).
"I think the No. 1 factor that we got with Danny is his success versus left-handers and what he can do in the box," the GM said. "Whether (Blue Jays manager John Gibbons) decides to put him at third, DH, first, he'll ultimately make that decision. I'm not concerned where he'll find spots for him. I think it will work out fine."
Also missing from the Blue Jays lineup is starting third baseman Brett Lawrie, who broke his right index finger after taking a pitch on the hand in Cincinnati five weeks ago.
Anthopoulos wouldn't say that having Valencia on the team would mean Lawrie could be permanently shifted to second base, a position he's played 32 games this season.
"I wouldn't read anything into it," Anthopoulous said. "Things change so fast.
"With respect to Brett, ideally you'd like to have any player be at one position the entire time but ... the great thing we see is that our players want to win and they're willing to play anywhere on the diamond," he added. "We've even had Encarnacion play left field.
"So it's been a really selfless attitude across the board. When Brett comes back we'll see what the health of the team is, we'll see who's playing well, and we'll come up with a game plan at that time."
Kratz, 34, is expected to report to Kansas City on Tuesday. He hit .198 with three homers and 10 RBIs in 34 games for Toronto, and .299 with a .354 on-base percentage through 27 games at triple-A Buffalo.
Hendriks, meanwhile, was 1-0 with a 6.08 ERA in three starts for Toronto. He was a triple-A All-Star this year at Buffalo, going 8-1 in 18 games (16 starts) with a 2.33 ERA.
While Anthopoulous said no other moves are in the mix as of now, he didn't rule out the possibility that more trades would be made ahead of the July 31 deadline.
"I think there's always a chance but I think all 29 other GM's would say the same thing," he said. "I think it's been very active in terms of phone calls, emails, texts, everyone seems to be exchanging ideas but that's expected. ... Trades are hard to make.
"I wouldn't say we're close to anything, but this deal came together fast so ... we're going to continue to talk to clubs."