The three teachers are Wipoj Saensuk, Anupap Banjong and Yutthana Phuthanonnok, according to Pol Lt Col Preecha Krongyut, the inspector at Phueng Daet police station overseeing the case.
Although the teachers have been accused of organising the gang rape and asked others to join in, they will not be charged with human trafficking, said Pol Lt Col Preecha.
The 16-year-old victim, a student at the same school, is serving as a witness in the first gang rape case against a 14-year-old girl.
The teenager said she had been raped by some of the suspects accused in the other case and the information she had provided corroborated that given by the first victim.
As of now, the second reported victim has been placed into the custody of the ministry of Social Development and Human Security.
Sirikarn Klongdee, the child psychologist caring for her said the girl was under an extreme amount of stress following her ordeal.
She has been given sedatives and psychological counseling, said Ms Sirikarn, adding that while the girl does not come from a poor family, her parents are divorced.
Both victims were reportedly raped on a number of occasions over a one-year period starting in March 2019.
The alleged gang rape case sparked national outrage when the grandmother of the 14-year-old girl filed a criminal complaint last week.
So far, police had pressed charges against five teachers and two male alumni. All have denied the charges against them and requested bail, which was granted.
One of suspects, Anupap Banjong has reportedly gone to stay at his father’s home in nearby Nakhon Phanom province.
Local media followed him and interviewed Manit Promdee, 77, his uncle who was shocked at the allegations against his nephew.
Mr Manit described his nephew as “polite man who couldn’t harm a soul”.
The uncle also told local media that Mr Anupap had told him that he had joined a party where the suspects drank alcohol together and met the girls.
He said his nephew denies, however, sexually assaulting them.
Meanwhile, police investigators scoured four sites connected with the alleged crimes; the school gym, the volleyball court, the teacher rooms and their private residences.
Pol Lt Col Preecha said they had recovered used condoms and a number of empty liquor bottles.
He said the police are prepared to take the victims and witnesses into protective custody in the event of witness intimidation.
Somsak Thepsutin, Minister of Justice, said officials from the ministry were already accompanying the victims and witnesses for their security.
Both victims are also eligible to receive B110,00 each - B40,000 for medical treatment, B20,000 for mental anguish and B50,000 for punitive damages.