Several questions have addressed taking advantage of an agreement between two countries to remain in Schengen longer than ninety days (example).
We now have a nearly complete list of such agreements, although I’m not sure all are still applicable. But I also wonder whether someone who was careful enough in travel planning could use such agreements to stay in Schengen for a very long time.
For example, the cited document shows ten countries having such agreements with USA—eight for ninety days, one for sixty days, and one for thirty days. So a hypothetical American who has a pathological addiction to Europe and sufficient funds might spend 89 days in Iceland, then more than two years going between those ten countries. Of course, that also assumes the nomad carefully avoids transiting through other Schengen countries, has copies of the pertinent agreements to show border folks, and doesn't encounter an official who decides to use their right to deny entry.
