Justices on the Massachusetts Supreme Judicial Court heard arguments Monday on whether hearings for 28 men accused of paying for sex at a brothel network with locations in Cambridge and Watertown should play out publicly.

The men are subject to a show cause hearing, in which a state clerk magistrate will consider whether they should face formal criminal charges. The hearings are typically not open to the public, according to the state.

Lawyers for the accused want a lower court’s ruling to make their clients’ hearings public overturned, saying that open hearings could harm their reputations.

Defense attorney Benjamin Urbelis argued that even if a clerk magistrate were to decide against charges for his clients, their public identification in an open hearing would lead to reputational harm.

“Once their name is out there in the media, livelihoods are going to be ruined, occupations likely lost. Their children are going to have to deal with this at school,” said Urbelis.

SJC Justice Gabrielle Wolohojian questioned whether her court had the “legal authority” to address Urbelis’ concern.

“Do I take judicial notice that undoubtedly these people will lose their jobs if probable cause is not found and no complaint issues?” Wolohojian said.

Urbelis also argued it was “improper” for federal prosecutors to have commented on the alleged clients. Federal charges were announced against the brothel’s alleged operators in last year. No federal charges were brought against clients, but the U.S. Attorney for Massachusetts claimed they included high-profile figures, including politicians.

Criminal proceedings against the accused clients have been handled at the state level. Urbelis argued that the U.S. Attorney’s initial comments on parties who had not been charged could set a bad precedent.

“That opens the door to now prosecutors are just going to leak information to the press and use that as a reason to have show cause hearings or even potentially grand jury hearing[s],” he said.

The push for open show cause hearings is being made by the Boston Globe and WBUR, who sued to make them public.

“If any of these hearings are held in secret, the public will assume that the people who got secret hearings got them because of connections or because of their undue influence because of their position in society,” said attorney Jeffrey Pyle, who represents the plaintiffs.

A decision from the Supreme Judicial Court is expected in the coming months.