Senator John Cornyn of Texas believes he can win a no-holds-barred Republican primary next year with his state’s hard-charging attorney general, Ken Paxton, by making the race all about the character of his opponent.

It’s a tall order, considering that Mr. Paxton has already faced down corruption allegations that played out in public when the Republican-controlled State House impeached him in 2023, only to see the Republican State Senate acquit him.

But in an interview with The New York Times, Mr. Cornyn said that there was much more about Mr. Paxton than what voters knew, hinting that the allegations of corruption and abuse of office that led to his impeachment were “just the tip of the iceberg.” Many more revelations would surface before the March 2026 primary, Texas’ senior senator said.

“This is going to be a test of whether character still matters,” Mr. Cornyn said, seated under a painting of Superman in the offices of a small sticker printing business in Waco, Texas.

Mr. Paxton remains a darling of the Republican voting base even after his 2015 indictment for securities fraud, a federal investigation into corruption allegations and his impeachment, during which former top aides accused him of using his position to benefit a friend and political donor who had helped Mr. Paxton conceal his extramarital affair.

But Mr. Paxton, now in his third term as attorney general, has survived each of those inquiries. Instead of being hobbled, he appeared to emerge stronger with primary voters.