Shkreli, 34, was suspended from Twitter in early January after he tweeted at Duca that he had an extra ticket to the presidential inauguration festivities of Donald Trump and suggested that Duca be his date.
Duca declined, forcefully.
Shkreli, apparently not happy with her rejection, then superimposed pictures of himself into photos of Duca and her boyfriend, making it appear as if Shkreli was her beau.
Duca then asked Twitter executives online why that was allowed on the social media platform.
Twitter suspended Shkreli's account in reaction to Duca's complaints.
He was later permanently banned, and then booted twice more after he set up accounts that were not in his own name.
But Shkreli has managed to communicate with his online followers via Facebook, where he continues to write posts and to stream himself in video from his apartment in Manhattan on some nights.
During the day, however, he has been on trial in Brooklyn, New York, federal court, where he is accused of defrauding a group of hedge-fund investors and then ripping off the drug company he had founded in order to pay those investors back.
His latest targeting of Duca came shortly after court recessed for Thursday night, after a day of closing arguments by a prosecutor and Shkreli's defense lawyer.
Despite eagerly running his mouth online, Shkreli has kept his mouth shut at his trial. Earlier this month, he agreed to an effective gag order by the trial judge after he ranted to reporters about the prosecutors in the case.
And he declined to testify at the trial.