Global Educational Management Systems (GEMS) has already bought two schools this term and aims to buy or build up to 40 in the next six months.
It has identified a number of schools or sites which it is seeking to buy and develop into co-educational private day schools.
GEMS has recently acquired Bury Lawn, in Milton Keynes, and Sherborne House, in Chandlers Ford, near Southampton.
The firm says it sees a gap in the education market in the UK and Europe and aims to offer a more affordable version of independent education. Its schools will cost around pound;5,000 per pupil per year.
Simon Cummins, director of schools for GEMS, said: "We are trying to get the best staff and will offer a salary 10 to 15 per cent above the going rate."
Susan Freestone, vice chairman of the Society of Headmasters and Headmistresses of Independent Schools, said: "This could become an issue and a serious concern but teachers will want to see how well the schools perform before they consider leaving to join them."
Terry Bladen, president of the National Association of Schoolmasters Union of Women Teachers, said: "The salary sounds very good but teachers would want to know what the conditions of service were before they consider leaving their jobs."