It's already been alleged Sir Cliff sexually abused a boy at a Billy Graham rally in 1985. The singer strongly denies the claims, and no charges have been brought against him.
But according to Sky News, the new developments in the case were revealed in a letter from South Yorkshire Police to Home Affairs Committee Chairman Keith Vaz.
The letter, dated 10 February, says: "South Yorkshire Police detectives are in very regular contact with Sir Cliff Richard's lawyers. Typically this involves a verbal update about once a fortnight.
"This is an investigation which has increased significantly in size since its inception. Sir Cliff Richard's lawyers are aware there is more than one allegation.
"In view of the expanding nature of the investigation, it would be premature and potentially misleading to predict a likely date when it will be concluded."
Sir Cliff Richard has also denied the latest allegations, in a statement he said: "I have no idea where these absurd and untrue allegations come from. The police have not disclosed details to me.
"I have never, in my life, assaulted anyone and I remain confident that the truth will prevail. I have co-operated fully with the police, and will, of course, continue to do so.
"Beyond stating that the allegations are completely false, it would not be appropriate for me to say anything further until the investigation has concluded, which I hope will be very soon. In the meantime, I would, again, like to thank everyone for supporting me through this unbelievably difficult period."
