The 86-year-old is to be tried again for allegedly assaulting a 14-year-old girl in 1971, a 13-year-old in 1983 and another teenager in 1978.
"We have decided to seek a retrial of Rolf Harris in relation to the charges of non-recent indecent assault on which the jury were unable to agree in respect of three of the complainants," Britain's Crown Prosecution Service said in a statement.
"A new, fourth count of indecent assault has also been added," it said.
The 86-year-old Harris is to be tried again for allegedly assaulting a 14-year-old girl in 1971, a 13-year-old in 1983 and another teenager in 1978.
The retrial date is set for May 15.
After studying art in London, Harris found fame in the 1960s when he secured his own television show after landing work at the BBC.
He scored a chart hit with the 1969 track "Two Little Boys", about two youngsters who grow up to fight in a war together, and performed his song "Tie Me Kangaroo Down, Sport" with the Beatles.
His success continued with the BBC's "Animal Hospital" in the 1990s and in 2005 he painted an 80th birthday portrait of Queen Elizabeth II.