Jockeying to replace state Senate President Stanley C. Rosenberg has already begun, with at least three senators lining up votes in case he resigns as soon as today amid the sex scandal involving his husband.

The intensifying effort to oust Rosenberg could push him to resign rather than face further embarrassment, insiders say.

Sens. Linda Dorcena Forry (D-Boston), Eileen Donoghue (D-Lowell) and Sal N. DiDomenico (D-Everett) each scrambled over the weekend to line up votes they would need to take the presidency, after Sen. Barbara L’Italien (D-Andover) said she’ll ask Rosenberg to step down at today’s caucus.

Senators plan to meet behind closed doors today and decide how to proceed with Rosenberg’s presidency and a pending investigation into the bombshell assault and harassment charges that have rocked the State House.

Rosenberg loyalists are still trying to bolster their two-term leader, but a number of senators are trying to pressure the powerful Democrat to relinquish his presidency or quit, feeling that it will be impossible to conduct a full investigation while he’s still in power.

Some lawmakers also are now calling for an outside investigation by a law enforcement authority, such as Attorney General Maura Healey, instead of appointing an independent investigator who would answer to the Senate.

And even those who like Rosenberg say he’s likely considered stepping down.

“I’m sure the president is spending a lot of time thinking of what’s best for the body and the future of the Senate,” said Sen. Donald F. Humason (R-Westfield).

Rosenberg’s husband, Bryon Hefner, allegedly groped three men and forcibly kissed a fourth, according to a Boston Globe column. The anonymous accusers had business before the Senate, believed Hefner could influence and control access to Rosenberg, and felt that they could not come forward without harming their careers.

Rosenberg said he will remain Senate president while independent investigators look into the allegations, but developments over the weekend might have changed that.

“I believe that for the sake of the institution, the Senate president should also step aside from the duties of the Senate presidency for the duration of any investigation,” said L’Italien, who is also running to replace U.S. Rep. Niki Tsongas (D-Lowell).

L’Italien has cited comments by some of Rosenberg’s alleged victims, who said they are uncomfortable coming forward and cooperating with the investigation if Rosenberg is still leading the state Senate.

Meanwhile, Rosenberg loyalists such as perceived successor Sen. Karen Spilka (D-Ashland) and Senate Majority Leader Harriette L. Chandler (D-Worcester) have pushed to keep the Amherst Democrat in power.

In a letter sent out Friday night, Chandler proposed that she “will take on the roles and responsibilities of the Senate President” in all matters related to the investigation into Rosenberg’s husband. She added that she can take over “under a provision of an order expected to be adopted by the Senate.”

But L’Italien and other senators have expressed concern about ongoing communication between Chandler and Rosenberg or his staff, especially as they push for a truly outside investigation.

“The firewall that was built in the past burned down, so you can’t guarantee it’s going to happen during this investigation,” Humason said of Rosenberg’s vow to stay out of the inquiry.

Sen. Sonia Chang-Diaz is also expressing concerns about the “limits” of any independent investigation, and said while it’s necessary, “It should not be entirety of the government’s response to these allegations.”

“The Senate has no actual jurisdiction over Mr. Hefner,” Chang-Diaz said in a statement on Twitter last night. “We also need to be humble and cautious in our assumptions about how impartial we can be, even when informed by an independent investigator.”

Hefner had been accused of boasting about his influence in Senate affairs in 2014, and Rosenberg responded by promising to create a “firewall” between his personal and professional life.

But some senators are questioning Rosenberg’s claim, and bristling at his declaration Friday that his husband “has no influence over policy, the internal operations of the Senate, or any Senate related business.”

“He absolutely had influence,” said one State House insider. “If Rosenberg can’t see that, then what else can’t he see?”