Experts failed to find any trace of the 11-year-old after digging up a grave in Coatbridge, Lanarkhire, earlier this month.
But it has now emerged Alexander Gartshore, suspected of murdering the youngster in 1957, may have buried her near a railway line just a few miles away.
Police believe the wooded embankment along the railway line between Dundyvan and Whifflet could hold vital clues.
Detective Chief Inspector Pat Campbell, leading the investigation, said his team had received dozens of calls following the failed graveyard search.
He said: "We know a lot more now than we did this time last week.
"We've already identified a handful of other locations in Coatbridge that would be of interest to us.
"We'll be interviewing all those who have offered information to gather as much knowledge as we can. If another likely site of disposal is identified by our investigation, we would want to look at that."
The development comes after a woman claimed Gartshore sexually abused her late brother in a shed near the tracks, close to an area known as the Slap Up.
She came forward after coverage of the dig at Old Monkland Cemetery.
The woman said: "My brother told me during an emotional discussion more than 10 years ago that he was a victim of Gartshore."
"He'd been led by the hand down the embankment to a shed or hut.
"I really agonised about telling his story because I'd promised not to, but in the end I felt that if it could provide a clue to a place and possibly find Moira for her family, I had to let the police know."