The lawsuits, which were filed anonymously in a state court, add to a wave of sexual assault litigation against the rapper, producer and record executive as he also faces federal sex trafficking charges in New York.
Thomas Giuffra, a New York lawyer who filed Thursday's lawsuits on the men's behalf, claimed Combs used his power and wealth to take advantage of the accusers and then ensured their silence through threats and fear.
Lawyers for Combs, 55-year-old founder of Bad Boy Records, said the claims are baseless.
"These complaints are full of lies," the lawyers wrote in a statement, declining to elaborate.
"We will prove them false and seek sanctions against every unethical lawyer who filed fictional claims against him."
The lawsuits involve incidents allegedly taking place from 2019 to 2022. The men, all identified as John Doe, say they were unwittingly served drugged drinks and then sexually assaulted by Combs and others.
They each seek a jury trial and to be awarded unspecified damages from Combs.
Combs has pleaded not guilty to federal charges that he coerced and abused women for years, using a network of associates and employees to hold drug-fuelled, elaborately produced sexual performances known as "Freak Offs" involving male sex workers.
Prosecutors say he then silenced his victims through blackmail and violence, including kidnapping, arson and physical beatings.
Combs has been seeking to be released until his trial in May but was denied bail a third time in November and remains in a federal jail in Brooklyn.
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