Additional charges, said to include bribery, could be raised as early as Tuesday, according to an official.
"Nothing has changed," said attorney Stephen Larson.
"My clients continue to rely on their constitutional right to a trial and will not be harassed by the threat of additional charges for the exact same behavior," said lawyer Tracy Minor.
A lawyer for Amy Colburn and Gregory Colburn, two parents accused of conspiracy to commit mail fraud and fraudulent service, as well as money laundering conspiracy, said they would not change their guilty plea either.
"At present, the addition of new charges seems vindictive and aims to discourage our clients and others from exercising their constitutional right to due process," said lawyer Patrick Hooper.
Douglas Hodge, Manuel Anriquez and Michelle Janavs agreed to plead guilty to conspiracy fraud and conspiracy to commit. money laundering, according to the US Attorney's Office in Massachusetts. All three have a plea hearing Monday.
At least 50 people involved in the case
Josh Girsky and CNN's Elizabeth Joseph contributed to this report.