At the mediation in September, 19 survivors flew in, at their own expense, from all over the country and gathered around a long wooden conference table in a Manhattan office. One by one, they recounted their stories, in graphic detail, in a room crowded with lawyers, Pingry board members and insurers. Displayed next to the victims were pictures of themselves at the ages they were when the abuse occurred, all big smiles and uneven little boy haircuts, oversized adult teeth still new in their mouths.

Mr. Crew said that he and his co-counsel, Peter B. Janci, believe all their clients have at least a “fighting chance” on the statute of limitations. But in mediation, he said: “It became clear that the insurance company was not going to offer much of anything on some cases, and Pingry was not going to make up the difference. That’s where it fell apart.”

“I’ve got a set of brothers where one is in and one is out,” he said of Pingry’s interpretation of the statute. “I’ve got plaintiffs who were in the same tent, at the same time, on the same night, with the same perpetrator — one is in, and some are out.”

In a statement, Nathaniel Conard, the headmaster of Pingry, said that the school, remained “committed to the ongoing mediation process.”

He said that the school recognized the difficulty of the mediation process for survivors. “We remain hopeful we can reach a resolution that helps the survivors heal and move forward,” he said, “while also keeping our school stable and healthy for the students it serves today, and the students it will continue to serve into the future.”

Marcy M. McMann, a lawyer for Mr. Alton, declined to comment.

The Pingry survivors say they are negotiating as a block, and they refuse to leave any member of their group with nothing.

“We’re just entries on a balance sheet,” Mr. Humphrey said. “You’ve reduced my life to a line item on an insurance claim like a roof or a damaged car. If I’m the only guy who gets a settlement, I’ll figure out how to split it between 21 men.”