During a Securities and Exchange Commission press conference Thursday concerning fraud charges against Nikola founder Trevor Milton, a member of the press asked the agency’s new Director of Enforcement, Gurbir S. Grewal, whether the financial regulators may take a “second look” at statements Elon Musk made about Tesla or its products on Twitter.

“You referenced CEOs making statements on social media making statements about their products,” asked the reporter, who did not identify himself. “Elon Musk has made a number of statements, some of which have been provably false, on Twitter. Are you going to take a second look at Mr. Musk’s statements under this administration or is that something you’ve been following closely?”

Grewal declined to speak specifically about any investigations or matters beyond the SEC’s Trevor Milton complaint. However, he noted that: “Regardless of the methods used by corporate officials, we will hold them accountable for materially false statements that they make, especially in cases where investors are hurt as alleged here.”

Musk’s habit of disseminating product and other company information on Twitter has inspired fans and critics alike to track his every interaction on Twitter, and his many promises and predictions shared there. Those statements have sometimes landed Musk and the company in hot water.

As part of its risk disclosures in Tesla’s most recent quarterly earnings filing, the company reminded shareholders that it was previously investigated by the SEC over Musk’s tweets in which he said he was planning to take his electric vehicle maker private at $420 a share, and had funding secured. Tesla and the SEC reached a settlement agreement over that matter originally in September 2018, and entered into a revised settlement agreement in April 2019.

The SEC has also investigated Tesla statements on Model 3 production rates — that investigation was resolved in Dec. 2019, the filing says — and has “issued a subpoena seeking information concerning certain financial data and contracts including Tesla’s regular financing arrangements.”