Keyes previously lived in Washington state before moving to Alaska in 2007 to start a construction business. He also owned property in upstate New York, near the Canadian border.
Ayn Dietrich, a spokeswoman for the FBI in Seattle, said agents are reviewing unsolved murders across the state to determine whether Keyes might have been responsible.
The FBI has consulted with behavior specialists to develop insight into Keyes' personality.
Their analysis is incomplete, but they know he was a loner who didn't have a clear pattern in selecting victims, who varied in gender and age.
Keyes told investigators that he was "two different people."
"The only person who knows about what I'm telling you, the kind of things I'm telling you, is me," he said, according to a March 30 police recording released by the FBI Monday.
Authorities described Keyes as methodical, in the Currier case taking days to find the perfect victim. He was also thorough in disposing of victims' bodies. Only Koenig's body has been recovered.
The FBI contends Keyes killed Koenig less than a day after she was kidnapped. Her body was recovered April 2 from an ice-covered lake north of Anchorage. Her disappearance gripped the city for weeks.
A surveillance camera showed an apparently armed man in a hooded sweat shirt leading her away from the coffee stand. Koenig's friends and relatives set up a reward fund and plastered the city with fliers.
Prosecutors said Keyes stole the debit card from a vehicle she shared that was parked near her home, obtained the personal identification number and scratched the number into the card.
After killing Koenig, Keyes used her phone to send text messages to conceal the abduction. He flew to Texas and returned Feb. 17 to Anchorage, where he sent another text message demanding ransom and directing it to the account connected to the stolen debit card, according to prosecutors.
Keyes made withdrawals from automated teller machines in Alaska, Arizona, New Mexico and Texas before his arrest in Texas, according to prosecutors. He was charged with kidnapping resulting in Koenig's death. Keyes could have faced the death penalty in her case.
Koenig's family said there was no apparent previous connection between the teenager and Keyes. Reached by phone Sunday, Koenig's father, James Koenig, declined to comment on Keyes' death.
Marilyn Chates, Bill Currier's mother, said police contacted her some time ago to tell her about Keyes' confession and to tell her that they believed the couple's killing was random. Authorities called Chates on Sunday to tell her of Keyes' suicide.
"After some thinking, our family has been saved the long road ahead — trials, possible plea agreements and possible appeals — and perhaps this was the best thing that could have happened," she said.
Ring reported from Burlington, Vt., and Associated Press writers Mark Thiessen in Anchorage, Alaska, Rebecca Miller in Philadelphia and Lisa Rathke in Montpelier, Vt., contributed to this report.