Griffiths was last week hit with a charge of not acting in the best interests of football by "singing about Hearts in administration" and the notice of complaint was updated after the SFA compliance officer watched fresh footage which emerged at the weekend.
This appeared to show the Scotland internationalist singing in a pub with Hibernian fans as they chanted a derogatory song about former Hearts player Rudi Skacel.
Griffiths, whose actions are also under investigation by police and his club, has now been accused of bringing the game into disrepute.
The 23-year-old - who joined Celtic from Wolves in January - was filmed with fellow Hibs supporters before watching his former team-mates lose 2-0 against Hearts at Tynecastle on March 30.
After the initial footage emerged of him singing "Hearts are going bust", Neil Lennon, the Celtic manager, last week warned Griffiths that the transgression was "his one strike".
Celtic stated on Monday that they took the fresh allegations "extremely seriously" and that they would be launching an internal investigation, while Police Scotland confirmed they had launched inquiries into allegations of "racist chanting by a 23-year-old Scottish Premier League footballer".
The SFA disciplinary hearing has been set in for April 24.