TORONTO – Joe Smith isn’t picky about his role in the bullpen although he’s certainly emerged as an important part of the Toronto Blue Jays’ stabilization over the past couple of weeks.

The veteran righty has pitched the eighth inning in six of the club’s past seven wins, his work especially important with Joe Biagini in the rotation and Jason Grilli seeing lower-leverage work while working through a rut. Of the many improvisations injuries have forced the Blue Jays to make recently, Smith as set-up man plays.

“Whatever we can do to get this thing rolling and get some wins here with five key guys out,” says Smith, a statement that’s more mantra for the Blue Jays, who after Tuesday night’s 6-0 loss to Cleveland are 10-10 since a dreadful 2-11 opening. “When we add them back in the mix, if we can sustain this a little bit right here, it’ll look pretty good.”

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But the knocks kept coming with Kendrys Morales leaving after two at-bats Tuesday due to left hamstring tightness that have him scheduled for an MRI Wednesday. Reinforcements may start arriving as soon as Sunday, with Aaron Sanchez on track for a return to face the Seattle Mariners.

Sanchez threw four innings and 60 pitches in a minor-league game Tuesday without any trouble with the fingernail on his middle finger, said manager John Gibbons, and barring a setback should be ready to go this weekend. If his finger allows him to pitch anywhere close to the way he did en route to an ERA title last year, that’s a huge boost.

His potential return would bump Mike Bolsinger – the ninth different starter the Blue Jays have used this year in comparison to just seven all of last season – who allowed two runs on three hits and four walks over 5.2 solid innings in the loss to Cleveland.

The right-hander fared much better than predecessors Mat Latos and Casey Lawrence, and rather than simply absorbing some innings, could easily have earned a win had Carlos Carrasco not been shoving opposite him.

“It was fun,” said Bolsinger, who hadn’t started since April 27 at triple-A Buffalo because a 90-pitch simulated game replaced a rainout last week to keep him on turn. “My family and everyone is from Chicago so we were sitting back and watching the games against the Indians (in the World Series). It was nice to go out there and face them and do well. That’s a tough lineup. Mentally I feel more tired than physically.”

Bolsinger, who is out of options, has four days of limbo ahead of him awaiting the verdict on Sanchez, although given the Blue Jays’ lack of starting depth, risking him on waivers may be a bad idea (the Blue Jays have spoken to free agent Doug Fister, but aren’t in on him right now).

Biagini threw four strong innings Sunday in his first big-league start and gets the ball again Friday versus Seattle. While the team seems committed to starting him during J.A. Happ’s continuing absence, the bullpen is undoubtedly thinner without him.

Happ is throwing at 100 feet but there’s no timeline yet for him to get back on a mound, so he remains weeks away from a potential return. Most likely to follow Sanchez back is shortstop Troy Tulowitzki, who hit and took grounders before the game Tuesday and could head out on a rehab assignment this weekend as he recovers from a strained right hamstring.

Russell Martin, placed on the disabled list Monday with a nerve issue in his left shoulder, might be ready soon after his 10 days are up, too. He underwent a procedure Tuesday that drained and injected cortisone into a cyst in his shoulder that was pressuring the nerve, causing, in part, the weakness he experienced in the area.

Josh Donaldson, meanwhile, continues to progress in Florida but there’s no clarity yet on when his strained right calf will be good to go.

Morales felt his hamstring tighten up running back to the dugout after a groundout in the fourth and any sort of absence will further stress a worryingly thin patchwork lineup that on Tuesday included just one regular infielder – Justin Smoak at first base – and managed all of four hits.

“I’m not so concerned so far,” Morales said through interpreter Josue Peley, although the MRI results can change that quickly. “We’ll see how it’s going to go from there. They’re going to tell me if it’s severe or not.”

As for the spate of injuries ravaging the roster, he said simply: “It’s frustrating for everybody.”

Amid the absences, Ryan Goins, Darwin Barney and Chris Coghlan have each provided difference-making moments, while Kevin Pillar, Smoak and Ezequiel Carrera have delivered beyond expectations, helping the team grind through the current crunch. But for things to turn around definitively, the Blue Jays will need Donaldson, Tulowitzki and Martin to get healthy and carry the load, in combination with consistent contributions from Jose Bautista, Steve Pearce and Devon Travis.

Until that happens, the Blue Jays will continue to scratch and claw out wins any way possible, looking for more players to step in and effectively fill voids the way Smith has during eighth innings of leverage.

“I told (pitching coach) Pete Walker when I got here, ‘Just tell me what inning you want me to be ready by, I’ll be ready. I’ll pitch whenever,’” said Smith. “I’ve done that my whole career, it doesn’t matter if I’m in the eighth or the sixth or the seventh, it doesn’t bother me. It’s not like I can get 300 saves. There’s no numeric value to go for.

“Obviously, when you know when you’re going to throw it’s a lot easier to get ready, doing all your stuff. But I’m still ready by the sixth every day – just in case.”

A wise approach given the way things have gone so far for the Blue Jays.