LAS VEGAS  — Investigators are looking into whether gunman Stephen Paddock scoped out bigger music festivals in Las Vegas and Chicago — and perhaps Boston’s Fenway Park — before setting up his perch in a casino hotel and raining deadly fire on country music fans.

Paddock booked rooms overlooking the Lollapalooza festival in Chicago in August and the Life Is Beautiful show near the Vegas Strip in late September, according to authorities reconstructing his movements before he undertook the deadliest mass shooting in modern U.S. history.

It was not clear if he contemplated massacres at those sites.

Investigators looking into Paddock also came across mention of Fenway Park, Boston police Lt. Detective Mike McCarthy said, though he provided no further details.

The details came to light as investigators struggled to figure out why the high-stakes gambler opened fire on a crowd of 22,000 Sunday night from the 32nd floor of the Mandalay Bay hotel casino in Las Vegas.

He killed 58 people and injured nearly 500 before taking his own life.

A federal official said authorities are looking into the possibility Paddock planned additional attacks, including a car bombing. The official wasn’t authorized to discuss the matter publicly and spoke to The Associated Press on condition of anonymity.

Authorities previously disclosed Paddock had 1,600 rounds of ammunition in his car, along with fertilizer that can be used to make explosives and 50 pounds of Tannerite, a substance used in explosive rifle targets.

Investigators have been combing through his background but remain stumped as to his motive.

The profile developed so far is of a “disturbed and dangerous” man who acquired an arsenal over decades, Sheriff Joseph Lombardo said. But investigators have been frustrated to find that he lived a “secret life,” Lombardo said, “much of which will never be fully understood.”

In other developments:

— In a rare concession on gun control, the National Rifle Association announced its support Thursday for regulating “bump stocks,” attachments that can effectively convert semi-automatic rifles into fully automated weapons. Paddock apparently used such devices during the bloodbath.

— The coroner’s office in Las Vegas would not release details of its autopsy on Paddock. Some behavioral experts have wondered whether the 64-year-old Paddock suffered from some kind of brain abnormality or had a terminal illness that prompted him to lash out.

The weekend before the massacre, he rented a room through Airbnb at the 21-story Ogden condominiums in downtown Las Vegas and stayed there during a music festival below that included Chance the Rapper, Muse, Lorde and Blink-182.

“Reasons that ran through Paddock’s mind is unknown, but it was directly at the same time as Life Is Beautiful,” the sheriff said.

Police were reviewing video shot at the high-rise to check Paddock’s movements. His renting the condo was curious because as a high-roller, he could have easily gotten a free room at one of the casino hotels on the Vegas Strip.

In early August, Paddock booked a room at Chicago’s 21-story Blackstone Hotel that overlooked the park where the Lollapalooza alternative music festival was being held, though there’s no evidence he actually stayed there, a law enforcement official said Thursday.