Kevin Liverpool, 34, and Junior Bradshaw, 31, are accused of crimes targeting 24-year-old Stone between January and June last year at her home in Devon, southwest England, according to the Press Association.
Exeter Crown Court heard that Bradshaw suffered from schizophrenia and had yet to enter a plea to charges of conspiracy to murder, conspiracy to commit GBH (grievous bodily harm) and conspiracy to commit robbery.
He is being held at a secure mental health unit pending further tests.
The court also heard that the mental state of Liverpool, who has pleaded not guilty to the same charges, was a "live issue" and a further psychiatric examination was being sought before deciding whether he was fit to stand trial in August.
Prosecutor Simon Morgan said it may be up to a judge to rule on whether they stand trial.
"It is clear that the defenses are not ready for trial and in those circumstances there is no objection to the extension of the custody time limit," Morgan said.
Bradshaw and Liverpool were arrested on June 13 last year close to the Devon home of Stone, whose 2004 album "Mind Body & Soul" topped the UK charts and who is worth an estimated nine million pounds ($14 million).
Judge Graham Cottle adjourned proceedings until April 16. A trial has been listed for August 6.
(Reporting by Mike Collett-White, editing by Paul Casciato)
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