Police and crime commissioners could help set up free schools aimed at preventing children from falling into a life of crime, Theresa May has said.
The Home Secretary also suggested the elected representatives could play a role in areas such as youth justice, probation and courts under an expansion of their influence.
Mrs May floated the proposals as she set out her vision for the next group of PCCs, who will be selected at polls for 41 forces in England and Wales in May.
In a speech to police leaders in London, she said: "I believe the next set of PCCs should bring together the two great reforms of the last Parliament - police reform and school reform - to work with and possibly set up alternative provision free schools to support troubled children and prevent them falling into a life of crime."
The Government is already preparing measures to allow PCCs to take on responsibilities for fire and rescue services in their local area.
Mrs May disclosed that she has been exploring what role they could play in the wider criminal justice system with the Justice Secretary Michael Gove.
She said: "This is something that I have long believed in and which a number of PCCs have shown interest in.
"As they say, there is a reason that we included the words 'and crime' in PCCs' titles.
"So after the May elections, the Government will set out further proposals for police and crime commissioners.
"Because, as a number of PCCs have argued, youth justice, probation and court services can have a significant impact on crime in their areas and there are real efficiencies to be had from better integration and information sharing."
In the speech to the Policy Exchange think-tank, she confirmed that the commissioners are "here to stay".
The first elected PCCs took office in 2012 with a remit including appointing the chief constable and setting force budgets.
Mrs May admitted there had been times when she feared she had "created a monster" with the reforms.
She said: "There has been good and bad over the last three-and-a-half years."
The Home Secretary mentioned controversies linked to PCCs, including the initial refusal by Shaun Wright to resign following revelations about child sexual abuse in Rotherham and the appointment of a youth commissioner in Kent, only for her to have to stand down after it was revealed she had posted offensive tweets as a teenager.
She also referred to "the decision of [Surrey PCC] Kevin Hurley to attack the leadership of his former chief constable and now director-general of the National Crime Agency, Lynne Owens, despite proposing pay rises for her over successive years".
She said: "These episodes have been disappointing and there's no doubt that some of them have brought the office of the PCC into disrepute.
"But unlike police authorities, police and crime commissioners are accountable to the people and in May each and every PCC will be judged individually at the ballot box."
However, she went on to insist that "there is now political consensus that police and crime commissioners are valuable and that they are here to stay".
Sara Ogilvie, of campaign group Liberty, said: "If this wasn't a speech by a senior Government minister, you would think it was satire.
"Tasking Police and Crime Commissioners to set up and run schools is a sure-fire way to estrange troubled children and fast-track them into the criminal justice system.
"Mixing police reform and school reform is a chilling distraction from the failure of the PCC project."