Ben, from Sheffield, was 21 months old when he disappeared on 24 July 1991.
Detectives said they would be "lifting all the earth" at the second site, 750m from where he was last seen and close to where the dig started last month.
They are investigating claims Ben may have been accidentally run over by a digger driver 25 years ago.
Officers are working on the theory that Konstantinos Barkas, who died of cancer in 2015, might be responsible for Ben's death.
Ben vanished from a farmhouse, which his grandfather was renovating, in the village of Iraklis.
Continued searches near the farmhouse were drawing to a close and the rest of the team will be focusing their efforts on the second site, police said.
Det Insp Jon Cousins said there was compacted material deposited over the last 30 years and the team "will remove this layer in the same [way] they excavated the first site".
Mr Cousins said: "I have made a decision that we're extending our stay here.
"We are going to be doing this to give me the confidence that I've done everything I can.
"The team are 100% behind this. And every single one of them, including the volunteers, are adamant that they are staying for this period of time. It's got to be done."
The team would remain on site for "at least two or three days", he said.
A team of 19 South Yorkshire Police officers, forensic specialists and an archaeologist have been excavating the area for nearly two weeks as a result of a television appeal in May, which brought the theory about Mr Barkas to the attention of the force.
Police searching for missing toddler Ben Needham on the Greek island of Kos have said they are extending their stay to continue exploring a second site.