The alleged victims came forward after Scotland Yard took the unusual step of issuing the name and photograph of Ernest Asamoah, 31, who detectives are looking for in connection with the rape of a 17-year-old Italian tourist. Police believe Mr Asamoah, who uses a serial of false names, is still living in London.
The Italian student was in a coma for five days after she jumped from a second-floor flat in Stoke Newington, north London, to escape from her attacker.
Scotland Yard revealed last week that Mr Asamoah, who was born in Ghana, had been questioned after the attack, but was released.
Since issuing details of the incident, three other women have contacted the police claiming they had been victims between May and July. In each case, they claim to have been lured back to the home of a man in Stoke Newington.
The police warned yesterday that the alleged serial rapist was "very plausible and charming" and preyed on students and older women.
In two separate cases, a woman was allegedly befriended by a man while travelling on a night bus and agreed to go back to his home and a second women was persuaded to go back to a man's flat after meeting him in Finsbury Park. One women was allegedly raped and the other indecently assaulted.
In a third incident, a man befriended two women while out walking and asked them back to his home for a drink. Once they arrived at his flat in Stamford Hill, Stoke Newington, only one of the women was allowed inside.
When the second started to shout for help, the man threatened her with a kitchen knife. She continued to call for assistance and two men came to her aid. The woman trapped inside the flat managed to escape as the two men scuffled with her alleged assailant.
A police spokeswoman said: "We issued a two-fold appeal for help to find Asamoah and to hear from other women who had been attacked. We are now investigating four possible cases; two of rape, one of indecent assault and one of unlawful imprisonment.
"These women ... have helped us form a clearer picture of the serial attacker and the way he operates. He has attacked students and older women. He is obviously very plausible, charming and friendly.
Mr Asamoah, a kitchen assistant who has worked in restaurants in Chelsea, Fulham and central London, is said to frequent the West End.
He uses a string of aliases including Samson Mensah, James Awuley, Ernest Amos, Ernest Asamiah and Paul Kofe Mensah. He also uses the first names Yaw, Ofsh-ene and Apenteng.