The cases against the 55-year-old father of four, who has taken leave of absence from a post at the UK's Oxford University following the accusations, have received huge media attention in France, where he has had a certain following among Muslims but attracted criticism from some politicians.
In the latest accusations, a Muslim woman in her 40s, who is referred to as "Marie", says he raped her on several occasions during rendezvous in hotels in 2013-14.
According to Europe 1 radio, she had told him that she had been an escort girl and that she had been one of the women who had sex with Dominique Strauss-Kahn and other men in a Lille hotel, leading to a court case in which the former IMF boss was found not guilty of pimping.
Ramadan, the grandson of Egypt's Muslim Brothers, used the information to bully her into sexual relations, the radio stations says.
He was charged with rape in the other cases on 2 February.
He denies the accusations and some of his supporters claim there is a conspiracy against him.
Retrial in sexual harassment case
A top appeals court in Versailles on Wednesday ordered a new trial in a sexual harassment case against a former PR chief for the town council.
It did not contest the guilty verdict against Rémy Le Gall, who was accused of harassment by four female employees but it did overrule the sentence of six months detention and 12 suspended.
The lower court had ruled that he could not serve the six months outside prison, for example by being electronically tagged, because he had denied harassment, while admitting making inappropriate remarks.
Wednesday's judgement ordered a retrial on the grounds that he had made his statements without realising that he had the right not to incriminate himself.