WASHINGTON — Amid another national wave of grief and outrage in response to a mass shooting, Sen. Pat Toomey (R., Pa.) plans to introduce a new version of his bill to expand background checks for gun purchases.

The move would bring back the one proposal to tighten gun laws that has come closest in recent memory to passing the Senate, and again place the senator who usually focuses on fiscal issues at the center of one of the country's most searing cultural debates.

"I probably will reintroduce it, but as you know, my goal is to move this process forward. My highest priority is to see if we can grow the vote," Toomey told reporters in Harrisburg on Wednesday morning. "It might take some tweaks to the legislation and I would be open to that because I do think it is reasonable to require a background check on commercial gun sales, and that's what my legislation would do."

Given Republican control of Congress — and the fact that his plan failed even when Democrats were in charge of the Senate — Toomey would almost certainly have to make his plan less restrictive to gain new votes.

The odds of success are uncertain, even with President Trump signaling support for tightening background checks. There have been similar calls for action after many mass shootings, only for opponents in Congress to stifle changes.

Asked if he sensed new momentum, Toomey said: "I don't know the answer to that, is the truth."

With teenagers leading  protests after a gunman killed 17 people at a Parkland, Fla., high school last week, gun-control advocates are again hoping for a political tipping point. A Quinnipiac Poll released this week found that 66 percent of Americans favor stricter gun laws, the largest share ever recorded by the poll.

Philadelphia-area  representatives joined the call for tightening background checks.

"While not a popular opinion with some Second Amendment groups, I strongly believe that background checks are worthless unless they cover every gun purchase. We can and must do more," Rep. Tom MacArthur (R., N.J.) said Wednesday. Rep. Ryan Costello (R., Pa.) would also support expansion, his office said, and fellow suburban Republican Reps. Pat Meehan and Brian Fitzpatrick have cosponsored a House bill to do so.

Trump on Tuesday tweeted that "we must now focus on strengthening Background Checks!"

It's unclear, however, what specific legislation he might support. The White House earlier said he backed a modest bill that would improve the flow of information to the national background-check system, but not run checks for gun show or internet sales. Lawmakers have also grown wary of Trump's shifting pronouncements.

Toomey's comments focusing on "commercial sales" — such as those by licensed dealers, at guns shows or online — suggest that he might include exceptions for unadvertised sales. That carveout was included when he first introduced his bill in 2013 with Sen. Joe Manchin (D., W.Va.), but last year Toomey hinted he was willing to cover all sales between "nonfamily members."

His original measure won 54 votes in the aftermath of the 2012 Sandy Hook elementary school shooting in Connecticut; it needed 60.

Since then the Senate has grown more Republican and more hostile to tighter gun laws. When Democrats brought Toomey's measure up again in 2015, it won six fewer votes than on the first attempt.