Baldwin, who’s also writing a fake memoir as Trump, didn’t name names, but it seemed clear that he was at least partially referring to Atamanuik, a name who’s been put forward by a number of people—including fellow Trump mimic Mark Hamill—as a good choice for the not-actually-on-the-table gig. (Comedy Central’s @Midnight, which hosted a televised version of Atamanuik’s show last year, recently featured Hamill’s tweet and endorsed his pick.) Atamanuik responded to Baldwin’s late-night claim on Twitter, and the actor promptly fired back:

As noted by Vulture, there’s been quiet tension brewing between Baldwin and Atamanuik for the last few months. Atamanuik auditioned for Saturday Night Live with Trump impression not long before Baldwin was named as the show’s permanent version of the then-candidate. Many have since noted that Baldwin’s take owes a lot to Atamaniuk’s, particularly his pronunciation of the word “China” as “Gyna.”

James Adomian, the Bernie Sanders to Atamanuik’s Trump, then joined the fray by accusing Baldwin of plagiarizing the take, provoking his own war of words.

Baldwin quickly responded:

As previously noted, nobody has actually offered anybody the job of playing Trump at the WHCD—this is all just hypothetical. Still, we can’t help thinking there’s an easier solution to this problem than proving who’s the Trumpiest Trump there is on Twitter. As multiple Twitter users have pointed out, there’s no reason not to just bring everybody down to D.C. and fill the Correspondents’ Dinner with dueling Donalds. It’s like people always say: You can never have too much Donald Trump.