Schools would retain their students but establish links, probably through new technology, with neighbouring institutions.
"I am not saying there will be sixth-form colleges that will drag sixth-form teaching out of the schools. But I think we will begin to work together and I hope universities will work with you," Sir Stewart told the university's first conference for secondary heads.
"If you have got Advanced Higher coming through in physics or biochemistry or literature, why should you not have specialist lectures from us or bring students in to experience hands-on some of the best equipment in the world. "
He believed Edinburgh would almost certainly have a network of schools and universities. "If you have 12 students across the city doing Advanced Higher Spanish, why could it not be done electronically?" he asked.
Original estimates of 10-15 per cent for the take-up of Advanced Higher were likely to be greatly exceeded, he said. "We would warmly encourage the sensible use of the sixth year and this is the best offer on the table because if folks become demotivated or deinterested in sixth year they have an awful job winding up once again to an intellectual challenge."
William Crossan, head of Campbeltown Grammar, feared students in many areas of Scotland would become "second-class citizens". Sir Stewart agreed it was unacceptable if Advanced Highers were not widely available but believed "the problem is there to have a solution".
Two-week residential courses might be one way to gain ground, he suggested.