The Camden County Animal Shelter's board of directors wants the family picked over 500 applicants to adopt "Prince Chunk" to sign a special contract.
The agreement, which hasn't been completed, could require mandated public appearances. Money generated may go to the shelter.
The Damiani family wonders whether the fat feline is being used as a "pawn." They also now question whether he weighed 44 pounds.
The Damianis say Chunk weighed 22 pounds when they took him to a veterinarian a few weeks ago.
Jennifer Andersch said the family's going public could jeopardize the adoption.
The cat, who once was called "Powder," was found lumbering around Voorhees after his owner lost her home to foreclosure last month and garnered national media attention because of his near-record weight.