Seated before an array of New York State senators on Monday, Lara Blume McGee was asked by one lawmaker why it had taken her so long to go public with the details of how Jeffrey Epstein had abused her.

She paused for a moment, another victim of Mr. Epstein’s by her side, and leaned forward to speak into the microphone in the State Capitol.

“Fear,” said Ms. Blume McGee, who had been 17 and an aspiring model when Mr. Epstein abused her. It took her about 20 years to come forward.

“Jeffrey Epstein was a great manipulator,” she added, explaining that she feared being sued and having her life ruined by his capacity for retribution.

Ms. Blume McGee was among four women who testified in the State Capitol about the trauma Mr. Epstein inflicted upon them and the lasting damage he did to their lives. The appearance of two of the women — Ms. Blume McGee and Carine Silva De Deus — had been expected, but two other women — Glendys Espinal and Alexandra Golematis — also came forward. Both said they were speaking publicly for the first time about their experiences with Mr. Epstein.

Their testimony comes as State Senator Zellnor Myrie, a Democrat from Brooklyn, seeks support for legislation intended to update state sex-trafficking laws. The goal, Mr. Myrie said, was to better equip the state to handle the kinds of crimes that Mr. Epstein was accused of committing by criminalizing the actions of people who helped perpetuate his behavior.

If passed, the laws would also allow Mr. Epstein’s victims to sue his associates and his estate in state court for punitive damages. State law prevents people from seeking punitive damages from the estate of someone who has died.

“Trafficking is not sustained by one single actor. It is not just Jeffrey Epstein,” said Kathryn Robb, a lawyer who has been pushing for these sorts of legislative changes across the country.

“It is a network that includes financial backers, businesses and other intermediaries, who often escape accountability,” she added. “This bill will disrupt that.”

Ms. Espinal, a Bronx native, said she first met Mr. Epstein during her sophomore year of high school, when she was brought in to give him massages. The demands from the financier quickly escalated, and she said she still has post-traumatic stress disorder from these interactions, which occurred between 2005 and 2008.

“What was going through my head at the time was just pure shame and intimidation,” she said.

Mr. Myrie’s bill, which has no companion legislation in the Assembly as of yet, is not state lawmakers’ only effort to reckon with Mr. Epstein’s legacy and the pain he caused hundreds of women.

Assemblywoman Pamela Hunter, a Democrat from the Syracuse area, and Senator Liz Krueger, a Democrat representing parts of Manhattan, have introduced a bill that would close what they call the “Epstein loophole.” In the state’s laws relating to prostitution, the buyers of a sex worker’s services, or those facilitating them, are excluded from punishment under the statute relating to people being punished for “advancing prostitution.”

“New York should act quickly and close the Epstein loophole, which would have prevented men like Jeffrey Epstein and Sean ‘Diddy’ Combs from being charged with trafficking at the state level,” Ms. Hunter said in a statement last month.

“This bill is necessary to ensure that traffickers and sex buyers are held accountable, while survivors of sexual exploitation are given the care and support they need,” she added, explaining that the law would also reduce punishments for those who perform sex work.

Mr. Epstein and his estate have settled several lawsuits with victims in recent years. The New York Times reported in February that a recent court filing showed that his estate was valued at $120 million, though the estimate might be an undercount.

Nathan Werksman, a lawyer for the women who testified on Monday, said that time was of the essence to change the law and give Ms. Blume McGee and others the chance to seek financial damages from Mr. Epstein’s estate.

Mr. Myrie’s bill, which the Senate Codes Committee passed on Monday, creates a one-year look-back period so that people can sue for actions that fall outside the statute of limitations. In this manner, it resembles the Adult Survivors Act, which in 2022 opened a one-time window in New York permitting people to file sex-abuse lawsuits after the statute of limitations had expired.

“The Epstein Estate is a finite amount of money that is dwindling every day, every week, and every month,” Mr. Werksman said.

“Jeffrey Epstein was able to escape criminal accountability, and his estate can escape civil liability if the estate dwindles down to nothing,” he added.

Lawyers for Mr. Epstein’s estate did not respond to emails seeking comment.