Schengen area visa issue

On behalf of a friend, I need advice from an ITN subscriber who knows the in’s and out’s of applying for a long-term resident permit in a Schengen area country, specifically Sweden. After staying in Sweden for 90 days, with the understanding that he could apply for a 6-month extension of his residence permit, this was denied – not only for Sweden but also for the 25 other countries in the Schengen group as they have a common visa agreement. Does anyone know how to solve the “90-day in the Schengen area challenge”? Otherwise, my friend would have to keep going in and out of the 26 countries in the Schengen area every 90 days.