Portuguese detectives have said they have checked out more than 400 tips across Europe and North Africa about Madeleine's disappearance. But the McCanns, who were named official suspects in the investigation earlier this month, have expressed concern that not all leads have been properly investigated.
They worried especially, according to British media reports, about two sightings on the same day by a Norwegian and a British tourist near the Moroccan city of Marrakech six days after Madeleine disappeared. Both tourists later complained the Portuguese police did not give their reports the attention they deserved.
Knuckey said that in cases of such international sightings, especially, private investigators could have the upper hand over regular police forces.
"If the Portuguese police make a request of the Moroccan police," Knuckey said, "it becomes a very long bureaucratic affair. Control Risks can cut all that out, because they're not hamstrung by diplomatic bureaucracy."
He added that private security teams are not hindered by the kinds of regulations that he said can sometimes constrict regular police forces.
"Again, the police are hamstrung with bureaucracy," Knuckey told ABC News. "When they're talking about informants, there are all sorts of guidelines and rules to abide by. It's all about dotting the I's and crossing the T's."
"The corporate sector is not required to adhere to that at all," Knuckey said.
Gerry McCann reportedly approached several private investigation companies in May, just weeks after his daughter went missing.
The McCanns have explicitly denied sending private investigators into Portugal after it became clear that it is illegal to hire private help in Portuguese criminal cases. But they have not denied reports that private investigators are looking for Madeleine elsewhere, such as Morocco and Spain, where a number of sightings have also been reported.
It is not clear how much a company like Control Risks Group would charge for its services, though one industry insider speculated to ABC News that it could cost up to $50,000 a month to keep the firm on retainer.
Financial supporters of the McCanns include billionaires Richard Branson and Sir Philip Green.
On the question of whether private eyes would have a chance at finding Madeleine nearly five months after she went missing, industry insiders couldn't agree.
"It's a long shot," said Peter Heims, the public relations officer and past president of the Association of British Investigators. "They're grasping at straws. But if you've only got straws to grasp at, well, then you gotta go that way."
Knuckey of Risc Management said private detectives would not be able to find Madeleine without a new lead in the case.
"They're never going to solve the disappearance," Knuckey said, "because to have a chance at doing that they would have to have access to all of the material that's been gathered by the Portuguese investigators. And that's not going to happen."
"But where they do stand a chance," he said, "is if there's a genuine sighting of Madeleine McCann. Then they will get people on the ground quicker than law enforcement will."
Ramm was more optimistic.
"I think it could make a difference," Ramm said of private investigators' possible involvement in the case. "Because I have real doubts that witnesses have been interviewed as thoroughly and professionally as they should have been."
"If very good, experienced homicide investigators or just good detectives get to those witnesses," Ramm said, "and go through it from the top, there is a chance that something has been missed."