The Senate voted to override President Barack Obama’s veto of a bill that allows families of 9/11 victims to sue Saudi Arabia, which means lawyers have started to move ahead with cases already pending in court:

James Kreindler, whose New York firm represents hundreds of victims’ families, said attorneys would soon file papers at the Second U.S. Circuit Court of Appeals in New York seeking to reinstate Saudi Arabia as a defendant in lawsuits filed shortly after the 2001 terrorist attacks and consolidated in the New York-based federal court.

“If we haven’t done it by today, we’ll do it Monday,” Mr. Kreindler said in an interview.

But what challenges do the plaintiffs face? The families and victims have sued across the country, but “consolidated into one suit in the Southern District of New York.” Lawyers have admitted that the 9,000 plaintiffs face an uphill battle:

“Although there is loose talk of 10 billion dollars’ worth of judgments against Saudi Arabia, in fact the deck remains stacked against the plaintiffs,” said Raj Bhala, a professor of international and comparative law at the University of Kansas Law School.

The plaintiffs must convince the court that Saudi Arabia had a hand in the terrorist attack that left almost 3,000 dead and tens of thousands injured. Unfortunately, the investigations and reports from the U.S. government have not shown direct involvement from the kingdom:

The 9/11 Commission found “no evidence that the Saudi government as an institution or senior Saudi officials individually funded” Al Qaeda. But the commission’s phrasing left some to speculate that there might be evidence of involvement by other, lower-ranking officials.

Some investigators have long believed that the various inquiries never unearthed the truth about several individuals connected to the Saudi government at the time of the attack, in particular a Saudi consular official in Los Angeles named Fahad al-Thumairy.

Mr. Thumairy, who had been the imam at the King Fahd Mosque in Culver City, Calif., had contact with two of the hijackers — Nawaf al-Hazmi and Khalid al-Mihdhar — in the months before the attacks. An F.B.I. document in 2012 concluded that he had assigned someone to take care of the two men during their time in the Los Angeles area.

Those documents also concluded that Saudi national Omar al-Bayoumi “helped the two men find an apartment in San Diego and cosigned their lease.” A document released last year stated that al-Bouyoumi has “ties to the Saudi Government and many in the local Muslim community in San Diego believed that he was a Saudi intelligence officer.”

Lawyers filed a new suit in D.C. “on behalf of the widow and daughter of a Navy officer killed in the attack on the Pentagon.” Kreindler told The Wall Street Journal he believes that case will join the ones already pending in New York.