The private school chain chaired by Chris Woodhead wants to make a dramatic increase in the number of schools it owns and double its turnover, just as the recession is starting to deepen.
The former chief inspector of schools founded Cognita in 2004. It now has 50 schools - 46 in the UK and four abroad - bringing in an annual revenue of Pounds 130 million.
The firm, which has previously said it expects to do well out of the downturn, has now revealed plans to almost double its turnover to more than Pounds 250 million by 2014, mainly by opening more schools overseas. Cognita promotes itself to parents as an education provider which charges fees below the market average.
The group already has two schools in Spain, and Stamford American International School, one of two it has in Singapore, is due to move into purpose-built premises this September.
Charles Robinson, the company's director of strategic development, returned from a fact-finding mission in Europe last week.
He said Cognita intended to open more schools in southern Europe, along with others in south-east Asia. "At the moment, 80 per cent of our business is in the UK, but we want to get turnover from both (UK and overseas) about the same," he said.
Cognita expects to open up to 20 schools abroad within the next five years. In addition, Cognita is expanding its Australian International School in Singapore by a quarter to 2,500 places.
Gems, another international company, confirmed that it also had expansion plans, although they are of a more modest nature.
Tayeb Chakera, its chief operating officer, said the Dubai-based group wanted to add three more schools to its 11-strong UK portfolio.
"Despite the recession," Mr Chakera said, "we're finding that, for parents, a child's education is the last thing they want to sacrifice."
The majority of its expansion plans are for overseas. The company, which has a Pounds 20 million turnover, already runs more than 70 schools in continental Europe, Africa and the Middle East.
Mr Chakera said Gems was considering opening schools in Australia and China for the first time.
The Pounds 11,000-a-year Royal Grammar School in High Wycombe, Buckinghamshire, is one of a number of grammars to have seen a sharp rise in inquiries as the recession hits parents.
Headteacher Roy Page said its sixth-form open evening attracted nearly three times the usual numbers.
"We had quite a lot of parents with children in independent schools," he said. "It's clear some are looking at ways to ease the financial burden.
The all-boys school has 70 boarding places.