Private companies should be encouraged to run state schools as profit-making enterprises under a "John Lewis-style" business model, a think tank suggests.
A report by the Policy Exchange says schools where staff were stakeholders - or partners - would create strong incentives to improve standards.
The proposal by the right-of-centre think tank is controversial and critics would oppose any such privatisation.
The Department for Education said there were no plans for this sort of measure.
Under the proposals by the Policy Exchange, half of any profits made by the schools would be distributed as a dividend to partners on an annual basis, while the remaining half would be reinvested into the running of the school.
The report suggests schools should operate outside the traditional structures which apply to teachers' pay and conditions. State-funded academies already have the power to set their own pay and conditions for staff.
Companies would only be able to draw dividends if the school met certain performance targets.
Schools would have to operate a social mobility test, for example, ensuring that 20% of pupils were eligible for free school meals.
They would also be prevented from selling off government-procured buildings and facilities for private gain.
The report, entitled Social Enterprise Schools, acknowledges that full profit-making in schools would be politically difficult to introduce immediately.
It suggests the government sets up pilot schemes across the country to test the effectiveness of social enterprise schools, initially in the most deprived areas of the country.
The head of education at the Policy Exchange, James Groves, said: "Given the huge challenges which our education system faces in the coming years, the government should continue to push the boundaries of the status quo.
"This report challenges the idea that there is simply a choice between for-profit and not-for profit schools.
"A 'John Lewis' model of school where private companies, including teachers and school staff, are encouraged to personally invest offers one such innovative alternative."
But a spokesman for the DfE said: "We have no plans to allow state-funded schools to be profit-making.
"The success of many academies in raising standards is built on philanthropic organisations using their expertise to turn around underperforming schools.
"We're more than doubling targeted investment at areas facing the greatest pressure on school places, to over £4bn in the next four years.
"Parents want to send their child to a good local school - that's we are building free schools, letting the most popular schools expand to meet demand from parents and driving up standards right across the system."