One way for the public to learn more about "what actually happened" at Bloomberg LP, Josephs said, would be for the firm to release women who complained about the work environment from strict nondisclosure agreements.
A company spokesman told ABC News that the company rarely settles disputes, preferring to take them to court.
When cases are settled, they generally include confidentiality provisions, so the extent of the alleged misconduct is not known, Josephs said.
Sakai, whose 1997 lawsuit accused Bloomberg of discouraging women from having children, settled her case against both Bloomberg and the company out of court for an undisclosed amount of money in exchange for her signing a nondisclosure agreement. Reached by ABC News, a lawyer for Sakai said she may be willing to share her story if the nondisclosure agreement were to be voided by the campaign.
ABC News has spoken with several women who expressed interest in telling their stories, but feared the prospect of facing retribution from the company for speaking out.
One former employee who worked at the company from 2003-2005, and spoke to ABC News on the condition of anonymity for fear of retribution, made similar allegations to those outlined in lawsuits over the years. The woman claims that a series of events, including a pregnancy, led her superiors to "sideline" her.
"Going to work was uncomfortable, everything was awful at that time," the woman said. "It was the worst thing that has ever happened to me."
When she left Bloomberg LP, she said the company asked her to sign a nondisclosure agreement in exchange for cash, but she declined.
"Everybody I knew was taking them," she said, referring to the confidentiality agreements.
ABC News asked Bloomberg through his campaign if he has considered releasing these women from their nondisclosure agreements. The Bloomberg campaign declined to comment.
