While the 10 named plaintiffs are seeking money from the city, the larger class is not.
The suit seeks $500,000 from the city as compensation for those expenditures.
The authorities are seeking at least $112 million in damages from the city and the state.
They said that would allow more time to seek additional help for the poor from the city and the state.
The bus dwellers are now seeking a permanent lot from the city.
The number of families seeking shelter from the city has grown rapidly over the last six years.
The hospital is also seeking rights from the city to add 720,000 square feet of biomedical research space on its campus.
A tax abatement sought from the city to help with costs was unsuccessful.
They are seeking damages from the city in a case that is to go to trial next month.
When the volunteers began recovering prehistoric material, the group sought help from the city.