Travolta's lawyer Marty Singer told the website: "As a result of the published lies about my client we expect some 'John Does' to come out of the woodwork and assert false claims."
The legal representative added that he has not yet been contacted by an attorney representing the fresh accuser.
The previous three men comprise of John Doe One, a masseur who has recently hired Gloria Allred to represent him after being dropped by his previous attorney.
There is also an Atlanta based masseur, who is being represented by Okorie Okorocha and Chilean-born former cruise line employee, Fabian Zanzi.
The gym personal trainer claims he would open the venue for the screen star when he was on location for a film shoot, after hours.
A close source said: "The gym was opened as a courtesy to John Travolta so that he could avoid the public yet maintain his fitness in this physically challenging role that he was doing at the time. The gym employee says that John Travolta groped and fondled him against his will."
Travolta has been married to actress Kelly Preston since 1991.
The couple's oldest child, Jett, died in 2009. They have two other children, daughter, Ella Bleu, and their toddler son, Benjamin, born in 2010.
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