The government wants to open 200 Academies by 2010
More schools should become independent state schools as they lead to improving results and are popular with parents, a right-wing think-tank says.
Policy Exchange says evidence from Sweden and the US shows parents are more satisfied with such schools.
The Tories say they will fund more schools run by charities, trusts and parents and teacher organisations.
But Schools Minister Jim Knight said the Tories were actually proposing education cuts.
The Policy Exchange report proposes allowing not-for-profit federations, charities, and parent or teacher co-operatives, to become "authorisers" of new schools, commissioning and overseeing them.
These would include elected mayors, local authorities, educational charities or universities.
It points to recent research by consultants PWC which suggests results at Academies are improving at a faster rate than in other schools.
"No one country has a perfect system, and we should blend together the most successful elements of school reforms in the US and Sweden, and the academies programme in the UK," said the report's co-author, Natalie Evans.
"The evidence suggests that allowing independent providers to run schools could help raise standards for the worst off, so we shouldn't rule it out for ideological reasons."
In Sweden, 12% of pupils are now educated in "free schools" - independent state-funded schools, and applications to open more are growing.
According to a survey commissioned by the Swedish government, parents view these schools more positively in a number of areas.
In the US, a similar idea formed "charter schools" - independent schools mainly in poorer communities.
The Tories have already said that they will broaden the current Academies programme, and take the idea of independent state schools further.
The Policy Exchange report says barriers to bidding for Academies should be removed.
But teachers' union the NASUWT voiced its concern at the report's suggestions.
General secretary, Chris Keates, said what worked in one cultural context was not guaranteed to work in another, and that politicians had an "obsession" with structures.
"This country already has one of the highest levels of devolved decision making to individual schools in the whole of Europe. Neither pupils nor the education system will benefit from more."
And Schools Minister, Jim Knight, said the Tories should "come clean" about their real plans based on Sweden's school system.
"The truth is that the Tories are proposing a risky free market experiment paid for by billions of cuts to our school re-building programme," he said.
They would "let under-performing schools wither and let the market decide".