More than 100 Russian athletes have written to the International Paralympic Committee (IPC) asking to compete at the Rio Games.
Russia were banned by the IPC after the McLaren report identified evidence of a state-sponsored doping programme.
The decision to ban Russia from the Games was upheld last week by the Court of Arbitration for Sport (Cas).
But the Russian Paralympic Committee (RPC) says scores of athletes are challenging that decision.
"More than 100 Russian sportsmen out of 266 who were selected for the Paralympics have filed individual cases with the IPC," Russian Paralympic Committee (RPC) vice president Pavel Rozhkov said.
London 2012 swimming champion Olesya Vladykina is believed to be among those who have contacted the IPC.
"There is no reason to ban me," said Vladykina, 28, on social media.
"I have sent the IPC documents and facts to allow me to participate in the Games in Rio individually. I will continue to fight for the truth and my name."
The IPC confirmed on Monday that it had received a number of letters from Russian Para-athletes and added that "internal discussions about the letters is ongoing".
Russian long jumper Darya Klishina was the only athlete from her country to participate in the track and field events at the Rio Olympics after she was cleared to compete by Cas.
Athletics' world governing body IAAF had banned Russian athletes from competing at the Games over doping concerns but Klishina took part after she was able to prove that her clean drugs-testing record was established in the United States, where she is based, rather than in Russia.
The Rio Paralympics begin on Wednesday, 7 September.