Manhattan public school parents are plotting a second battle against the multimillionaire charter school benefactress Courtney Ross, reprising a 2006 fight that ended only after intervention by the Assembly speaker, Sheldon Silver.

The issue, now as in 2006, is whether Mrs. Ross’s charter school, the Ross Global Academy, should be given space in a public school building. The one new development is that because the charter school now has an almost two-year track record, and paper trail, this year’s fight is likely to include some unsavory details about the school’s financial and educational history.

The 2006 discord ended with parents at a Lower East Side school for the gifted and talented ousting Ross Global Academy from their building. The school was instead placed in the basement of the Department of Education’s Tweed Courthouse headquarters.

Ross Global Academy has outgrown that space, and so the city is proposing once again that it school should move building , this time on East to a public school building on 25th Street whose current occupant, the School for the Physical City, is being phased out.

That plan is not likely to pass without a fight from Lower Manhattan parents who are furious that the city would give up precious space in a crowded school market — high on demand as more and more condominiums crop up, but low on supply — to a charter school.

“People are outraged,” the executive director of the group Class Size Matters, Leonie Haimson, said.

“Public spaces should be used for public schools,” a parent at the nearby elementary school P.S. 116, Mary Silver, said. “Charter schools are a different animal, and in this case I understand that the Ross Academy is being funded by Courtney Ross, and you know, she has different resources.”

Mrs. Ross, the widow of a former Time Warner chairman, Steve Ross, owns a second private school in the Hamptons.

School officials said parents are the mistaken to place their hopes on the East 25th Street building for crowding relief. The city’s lease on that building is expiring at the end of the next school year, and there are no plans to re-sign it, so any school that enters it will have to leave by the end of the year, a Department of Education spokeswoman, Melody Meyer, said.

Parent activists countered that they would welcome a year’s worth of space.

“We’ll take next year,” a parent at P.S. 116 who is also a member of Community Board 5, Layla Law-Gisiko, said.

The ugliest part of the battle parent activists are plotting is likely to be claims about the charter school’s quality.

City Department of Education reports on the school, posted on the Internet and now being scoured by the activists, detail two tough years marked by financial mismanagement; weak curriculum, and an unsettling amount of staff turnover. A recent report says the school’s board of trustees “failed to provide effective oversight” and concludes that the school has “been on an overspending spree since its inception.”

It details large bonuses paid to administrators who served short terms, such as nearly $25,000 paid to a principal who served 47 days and more than $50,000 to a principal who served for less than two months.

The current principal, Stephanie Clagnaz, said Ross Global Academy has seen much positive change since the report was written, and pointed to a follow-up report by the department that concluded the board had tightened its oversight “considerably,” that curriculum has improved, and that the financial situation is also looking brighter. The report says the school’s short-term liabilities are now just under $300,000.

Ms. Clagnaz said almost 100% of current students have said they plan to return to the school next year.

She said that, of 350 students who applied for 100 available seats in next year’s classes, most of the students are from District 2.

Ms. Clagnaz said she understood the parents’ concerns, “Space in New York City for public schools is very, very tough to get,” she said, then added: “It’s kind of a shame that there are adults anywhere that are pitting one group of children against another group of children.”