TMZ has obtained multiple new lawsuits, all filed by the same New York-based attorney (not Tony Buzbee) ... with the unnamed plaintiffs all claiming Diddy drugged and then sodomized them -- with the earliest claim dating back to 2019.

While there's nuance to each claim, they all share similarities ... with the accusers saying they went to party with Puffy and his crew -- two claiming they went to hotels with him and one claiming they were raped at his residence in the Hamptons.

All three accusers say they accepted alcoholic beverages from Diddy ... before claiming they quickly became disoriented and passed out -- only coming to when Diddy was "sodomizing" them.

One man claims the alleged rape was filmed by associates of Diddy ... who then paid him $2,500 on behalf of Diddy. The other two accusers do not say they were paid.

According to the lawsuits, none of the alleged victims spoke up in the aftermath of the incidents due to fear and humiliation.

As we said, two of the accusers claim they were raped in hotels -- with one saying Diddy sodomized him in his suite at the Park Hyatt Hotel on 57th street ... the same hotel where federal agents arrested Diddy in September.

These new lawsuits against Diddy add to the growing list he's facing ... though it's worth noting again that these alleged encounters took place in recent years -- whereas earlier claims dated back as far as the early 1990s.

Diddy's currently locked up in MDC Brooklyn on racketeering conspiracy, sex trafficking and transportation to engage in prostitution charges. His attempt to be released on bail was denied again last month, so it looks like he'll remain locked up until at least his trial in May.