Asked numerous times if Jake Burger, who a couple years ago did a little practicing at second base in the minor leagues, could be an option to play second base this season, Pedro Grifol seemed to have zero appetite for the idea.

“We haven’t discussed that,” Grifol said earlier this month when asked about Burger playing second base. “The game has changed a little bit in that aspect, because there’s no shifting. In recent years, you can do some of those things and still cover a significant amount of territory on that side of the field. But the game has changed.

“We haven’t discussed (it). That doesn’t mean we won’t at some point, if we had to, but at this point, we haven’t discussed that.”

Well, the discussions have apparently been had, as Burger has been practicing at second base lately. With Eloy Jiménez departing for a rehab assignment with Double-A Birmingham on Tuesday — and Elvis Andrus still on the injured list — there could soon come a time when Burger gets some run on the right side of the infield.

Grifol said Jiménez will spend 3-4 days in Charlotte before they evaluate if he’s ready.

Elvis Andrus will need a rehab assignment and it probably won’t be until next week.

Yes, Jake Burger is taking ground balls at second base. Grifol sounded open to it on an occasional basis

— James Fegan (@JRFegan) May 23, 2023

This is all because Burger’s kept hitting. His .997 OPS in 31 games heading into Tuesday’s 4-2 win in Cleveland elevated him to the status of one of the White Sox’ best hitters. But he didn’t make the Opening Day roster because there was no position for him to play. After doing impressive fill-in work while Yoán Moncada was injured earlier this season, Burger is once again a man without a spot, unless you count the DH spot, which was supposed to be occupied by Jiménez.

The White Sox can’t afford to field a lineup without Burger at this point. Meanwhile, Jiménez is close to returning to the big league club after a weeks-long recovery from an appendectomy. Gavin Sheets, too, has been a consistent offensive presence. And Moncada and Andrew Vaughn remain parts of both the short- and long-term planning on the South Side.

This is the classic “good problem to have,” or as Grifol’s predecessor, Tony La Russa, would often put it: “Too many good players.”

This might be a “good” problem, the type the White Sox have been begging for after a litany of bad problems led to miserable April and currently have them sitting 10 games below .500. But it’s a problem, nonetheless, Grifol tasked with squeezing all of these hitters into his lineup as often as possible. That Burger and Moncada, as well as Sheets and Vaughn, or Sheets and Jiménez, play the same position makes that a challenge. The DH spot offers only so much relief, considering the bat-first, glove-second descriptors accompany Jiménez, Sheets and Burger.

Moncada won’t be moved from third base, his defense typically sensational and his bat currently lodged in the middle of the order. Vaughn, too, would seem destined to play the vast majority of the time at first base, a top-three draft pick treated as a franchise cornerstone.

Oscar Colás’ rough first month as a major leaguer and subsequent demotion to the minor leagues has offered an avenue for Grifol to more easily fit all these pieces together, though the manager surely would have preferred Colás produced up to the hype and what the White Sox witnessed during the spring, when the rookie won the everyday gig.

Andrus, sidelined with an oblique injury, is nearing a rehab assignment of his own, but the second baseman’s bat has been slow to recreate what it did after the White Sox acquired him late last summer. After hitting nine home runs in 43 games last year, he’s got a career-worst .534 OPS through his first 39 games this season, his first at a new position after a decade and a half as a big league shortstop.

Andrus’ status as a veteran voice in the clubhouse and his lengthy resume of big league success mean he’s unlikely to simply be jettisoned from the roster, like Jake Diekman was earlier this year. But that lack of production might open the door for some moonlighting by one of the team’s hot hitters, as unsuited for the position they might be.

Burger is the one who might be deployed there, if his recent work at the position is any indication, not as an experiment, as Grifol described it earlier this year, but as a poor-fit option to keep his bashing bat in the White Sox’ lineup. Even in the glare of Tuesday’s five-strikeout performance in Cleveland, he’s hit so well it’s impossible to sit him on the bench and use him for nothing other than Moncada’s rest days. And so, as a possible solution, here’s something Grifol didn’t want to do. In bringing up the new rules banning the shift, Grifol explained that the White Sox are unable to make up for any deficiencies in Burger’s range by sliding Tim Anderson to the other side of the second-base bag.

Swapping defensive confidence for offensive thump might be in play in Colás’ old stomping grounds in right field, too. Sheets has been the one to mostly man the position since Colás was sent down at the start of May. His presence there hasn’t been as calamitous as panicky fans might have imagined — his lowlight-reel tumble to the ground in Minnesota excluded — but he hasn’t proven himself able to cover the same ground or make the same plays that someone like, say, Adam Haseley or Billy Hamilton can, and there’s a reason those two have been subbed in as late-game defensive replacements in right fairly often.

Sheets’ bat, though, has made his frequent appearances in right field plenty palatable. The question is whether Jiménez will do the same.

Long derided for what he does when he plays the outfield, whether resulting in comical misplays or serious injuries, he seems destined for far more run in right field than was plotted at season’s start. Grifol has been talking about Jiménez playing right field since the White Sox introduced Andrew Benintendi as their everyday left fielder in January, but he’s only been out there three times since the regular season started. By the manager’s own admission, however, Jiménez will be out there more after his return from this weekend’s rehab assignment.

“That’s a part of his rehab, too, he’s going to play some right field. So it’s not like before, ‘We need the bat (only), get in the lineup (as a DH with sore legs).’ We need him to play some right field, as well,” Grifol said over the weekend. “He won’t play out there all the time, but he’ll play out there enough to be able to mix and match what we want to do.”

With Grifol’s planned DH becoming his new right fielder, the skipper is able to use that DH spot for Burger or Sheets, while keeping Moncada at third and Vaughn at first. Rolling the dice with Burger at second base allows everybody to get into that lineup at the same time.

Of course, this will provoke the obvious cries of defensive malpractice. Sheets and Jiménez have already had their bad moments in the outfield in their short major league careers, while Burger would be a complete experiment at second after his own history of at-times-shaky play at third base — the very thing that kept him from the Opening Day roster and regular big league appearances prior to this season.

That would work against one of the main objectives of Rick Hahn’s offseason, to improve a defense that was among the worst in baseball during the massively disappointing 2022 campaign. But considering that 10 games below .500 is significantly more panic-inducing than being at .500, it makes sense that the White Sox would swallow downgrading defensively in order to achieve the ultimate goal of Hahn’s rebuilding project: assembling a collection of hitters that crush opposing pitchers on a nightly basis.

Indeed, that was the idea last year, that a power-packed lineup would cancel out any defensive deficiencies. Instead, mostly everyone on the roster experienced down to career-worst years.

The White Sox are far from being that power-packed lineup right now, exhibited by their three-hit blanking at the hands of the Guardians on Monday night and a better but similarly offensively lacking effort in Tuesday’s win. But their numbers are better than they were during the team-wide power outage of 2022, and inserting more thump across the board could only help the White Sox dig out of the early season hole they dug for themselves.

Who knows if this strategy will work, as Grifol already seems to have converted from his “no Burger at second base” stance to a more lenient one in the name of stocking the lineup with big bats. That has its own flip side, and should a greater sample size of Burger at second and Jiménez in right yield the sorts of defensive problems plenty would be rightful to fear they could, such an experiment could be over in a hurry.

But the White Sox need something right now, anything to help turn their season around. If backpedaling defensively to crank things up offensively is a way to do it, then let the fun begin.