The two most powerful Democrats in the Massachusetts Legislature said they are still considering whether to tinker with a voter-approved law that grants more power to the State Auditor’s Office to investigate the inner workings of the House and Senate.

House Speaker Ron Mariano and Senate President Karen Spilka again indicated Wednesday they could ask their members to make changes to a successful ballot question that was championed by State Auditor Diana DiZolgio, a former state lawmaker who regularly clashed with leadership.

Mariano said he is discussing with Spilka ways “in which we can improve the perception that we are a transparent body” — a nod to a widely-held belief that the state Legislature is one of the most opaque governmental bodies in the country.

“We will be discussing different opportunities to make some changes,” Mariano said of the audit law. “We are currently, right now, talking about different things. We had a meeting this morning.”

In the days after residents voted to approve the ballot question, DiZoglio reignited her effort to probe the Legislature and gather missing information that lawmakers did not turn over during her first attempt at investigating the two chambers.

In a Friday letter to Mariano and Spilka, DiZoglio said the renewed audit will focus on “high-risk areas” like state contracting and procurement procedures, the use of taxpayer-funded nondisclosure agreements, and legislative financials.

“We ask that all requested records and information be made available to use within 72 hours of the date of request,” DiZoglio wrote.

Spilka said the two chambers plan to respond to DiZolgio’s letter “shortly” and any changes to the voter-approved audit law will “align with the fundamental principles and responsibilities of our Mass. constitution, especially the separation of powers.”

The two legislative leaders left the door open to changing the ballot question before Election Day, which prompted a fierce backlash from DiZoglio.

“They’re trying to discourage people from voting their conscience by telling them that their vote doesn’t matter, essentially, that they’re just going to ignore the will of the people anyways, and it’s unacceptable,” DiZoglio told the Herald two days before voters were set to hit the polls.

After it was clear the ballot question would succeed on Nov. 5, Mariano and Spilka said they were considering their next steps.

“Consistent with how the Legislature has moved forward with every voter-approved ballot question in the past, we will consider next steps regarding how to best respect the Question 1 election results in a manner that aligns with the fundamental principles of the Massachusetts Constitution, including separation of powers,” the duo said in a statement last week.