The Supreme Court grappled Wednesday with an appeal from an Oklahoma death row inmate who even the state’s conservative attorney general believes should not be executed, with some justices signaling a willingness to let state courts further review allegations that prosecutors withheld evidence in the case.

After nearly two hours of oral argument, it was clear the court’s three-justice liberal wing would side with Richard Glossip, 61, who was convicted of arranging the murder of Barry Van Treese in 1997. At least two of the court’s conservatives — Justices Clarence Thomas and Samuel Alito — signaled deep reservations with Glossip’s appeal and indicated they would oppose him.

Of the conservatives, Justice Brett Kavanaugh seemed the most sympathetic to Glossip, who has been scheduled for execution nine times and has eaten his last meal three times only to have his execution stayed.

That means the high court’s majority decision will likely come down to how Chief Justice John Roberts and Justice Amy Coney Barrett view his case.

Glossip’s conviction rests on the testimony of Justin Sneed, the man who killed Van Treese with a baseball bat in a hotel.

In exchange for avoiding the death sentence himself, Sneed implicated Glossip as the mastermind of the crime. But years after Glossip’s conviction, the state disclosed evidence that Sneed was treated for a serious psychiatric condition — a revelation Glossip’s attorneys say prosecutors withheld from the jury.

“He lied on the stand,” said Justice Elena Kagan, a liberal, noting that Sneed testified that he never saw a psychiatrist when, in fact, it was a prison psychiatrist who had prescribed him lithium to treat bipolar disorder. “Your one witness has been exposed as a liar.”

Thomas, who, along with Alito, led the questioning opposing Glossip, repeatedly asked why investigators looking into the case years later didn’t more thoroughly question the prosecutors involved at the time about notes they had taken indicating they knew about Sneed’s diagnosis and treatment.

“They are central to this case,” Thomas said of the prosecutors. “It would seem an interview of these two prosecutors would be central.”

That could open a potential solution for the court. Several members, including liberal Justice Ketanji Brown Jackson, discussed the possibility of sending the case back to state court to further review the meaning of the notes prosecutors took at the time.

“Why wouldn’t we send it back for an evidentiary hearing?” Jackson said at one point. “It’s my understanding that there’s never been a court determination of any of these facts.”

Death penalty cases are getting more attention at SCOTUS

The case has landed at the Supreme Court at a moment when the death penalty — and the court’s approach to it — is the focus of unusual attention and scrutiny.

A divided decision last month allowing Missouri to execute Marcellus Williams — despite the objection of prosecutors — drew sharp criticism from groups opposed to the death penalty.

Several other death penalty appeals, meanwhile, are pending on the Supreme Court’s docket. On Friday, the court granted an appeal from Ruben Gutierrez, a death row inmate in Texas who was denied an opportunity to seek post-conviction DNA testing. The case will likely be up for oral argument early next year.

The justices will also be deciding whether to hear arguments in other death row cases when they convene on Friday for their weekly, closed-door conference meeting. One involves an Oklahoma woman convicted of killing her husband who says prosecutors sex-shamed her during her trial, referring to her in court as a “slut puppy” and holding up her underwear for the jury. Another involves an Alabama man who claims he is intellectually disabled and therefore ineligible for execution under Supreme Court precedent.

The Glossip case is arguably the highest profile to reach the court in years, and it drew two of the most experienced Supreme Court lawyers in the nation. Seth Waxman, a former solicitor general, is arguing on Glossip’s behalf. Oklahoma Attorney General Gentner Drummond, a Republican who supports sparing Glossip, was represented by Paul Clement, also a former solicitor general.

Even though Drummond called for a new trial, the Court of Criminal Appeals of Oklahoma upheld Glossip’s sentence, ruling that the evidence at issue wouldn’t have changed the outcome of the case and that Glossip’s attorneys knew that Sneed was taking lithium.

Kavanaugh, who could prove to be a key vote, raised a concern with that position. Kavanaugh said he was having “some trouble” with the idea that “it still wouldn’t have made a difference to the jury had they known that Sneed was bipolar and that he had lied on the stand.”

Justice Neil Gorsuch was recused, meaning that only eight justices will decide Glossip’s fate.

Before the justices can even reach the merits of Glossip’s appeal, they must first resolve a procedural hurdle: Whether the state court erred in ignoring Drummond’s admission of error. Defending the conviction and sentence, attorney Christopher Michel argued that the state court decided the case in a way that leaves the Supreme Court little room to rule in favor of Glossip.