HARRISBURG — Amid a high-stakes inquiry ordered by Gov. Wolf into whether Lt. Gov. Mike Stack and his wife mistreated some of their employees, a group of senators is pushing to change the way the public elects candidates for the state's No. 2 job.

The senators, led by David Argall (R., Berks), announced legislation on Tuesday that would allow Pennsylvania's gubernatorial nominees, like those running for U.S. president, to choose a running mate for lieutenant governor in future elections.

Argall said he was pushing the legislation due to the "tumultuous" relationship between Wolf and Stack, both Democrats. He noted numerous media accounts that indicated the two men rarely speak.

"Let's be honest, this is embarrassing," Argall said at a news conference in the Capitol. "This is not how the top two members of the executive branch should operate to get things done for the people of Pennsylvania."

The legislation would require an amendment to the state constitution, meaning the bill would have to pass in two consecutive legislative sessions and then be put to a voter referendum. As a result, it couldn't take effect until after next year's gubernatorial election.

If the legislation becomes law, future candidates for governor would be able to select their running mates after winning their party primaries.

The legislation has 15 cosponsors, including two Democrats, Argall said, adding that several other states grant gubernatorial candidates the ability to choose running mates. According to the National Lieutenant Governors Association, Pennsylvania is among only 13 states where lieutenant governors are elected during the primary election independently of the governor. They are then yoked together on the general election ballot.

Argall said the amendment is inspired solely by the icy relationship between Wolf and Stack, and not any of Stack's alleged personal misconduct. He argued that the position of lieutenant governor is a waste of taxpayer money if the officeholder does not get along with the governor.

"With these kinds of dire economic circumstances, we cannot afford to waste one more nickel on a system where the No. 1 and No. 2 elected officials in the executive branch fail to work together as a team," Argall said.

The bipartisan efforts are viewed by the senators as more of a step in the right direction than a utopian solution.

Sen. Mike Folmer (R., Lebanon) acknowledged, "There's no perfect way to do this, but this is an improvement."

J.J. Abbott, spokesman for Wolf, declined to comment on whether Wolf would support the amendment.

Stack spokesman James Kurish said the lieutenant governor would support the measure if it is part of a more "holistic" approach to reforming elections, one that includes changes to the state's redistricting process, among other changes.

The inquiry into Stack became public in April. At the time, Wolf said he had asked the Office of the Inspector General to investigate whether Stack and his wife, Tonya, had verbally abused or mistreated employees who work at their taxpayer-funded residence outside Harrisburg, as well as the state police detail that protects them.

The status of the OIG's report is unclear. Wolf has signaled that it is not complete.

Stack has apologized for what he has called "Stack moments," saying he sometimes becomes frustrated and snaps in anger.

Wolf has confirmed that he asked Stack several times to improve his behavior before ordering the official inquiry. As the investigation progressed, Wolf took the extraordinary step of yanking the Stacks' state police detail and scaling back staffing at the lieutenant governor's residence.

Early on, the governor said that he intended to make the report public. That was before Stack's office confirmed last month that Tonya Stack had checked into a mental-health facility to seek treatment.

Contact Logan Hullinger at l.r.hullinger@gmail.com or 814-319-5158.