The federal authorities investigating Diddy to possibly get a criminal indictment against the music mogul are chugging along ... issuing a new grand jury subpoena related to a hotel in Florida.

According to new legal docs, obtained by TMZ, federal prosecutors from the Southern District of New York got a subpoena requiring the fancy Miami hotel to cough up documents and other evidence related to Diddy.

Diddy and his ex Daphne Joy are both named in the subpoena. The subpoena calls for the hotel to hand over reservation records involving Diddy, Daphne and other associates of the Bad Boy Entertainment CEO.

The subpoena specifies the period from January 1, 2008, to the present, asking for check-in and check-out dates, room numbers, guest preferences and requests, and billing information, including room service.

Federal prosecutors also requested email and mailing addresses and phone numbers, along with forms of payment, such as cash and credit cards.

Prosecutors further asked for computer IP addresses and logins for the individuals, as well as copies of their identifications and vehicle information. What's more, the feds inquired about surveillance footage at the hotel.

The new subpoena was issued only a couple weeks ago ... so it looks like the authorities are still hard at work on the Diddy probe.

As we reported in March ... Homeland Security agents raided Diddy's homes in Miami and Los Angeles during an ongoing investigation into the record exec for alleged sex and narcotics trafficking.

TMZ also confirmed a federal grand jury was convened and witnesses were notified they could be called to testify in the Southern District of New York.

Meanwhile, Diddy's been named in 8 lawsuits accusing him of sex trafficking, sexual assault and physical abuse. The most notable suit was brought by his ex-girlfriend, Cassie, which they quickly settled.