In prior non-archival work, Blevis and Blevis, 2022  cite a notion from marketing research about linear and non-linear thinking. In the marketing research, we learn that people oftentimes expect linear relationships when non-linear relationships hold. These expectations can lead to poor business decisions. These same principles apply to interaction design and supply the theoretical underpinning for a framework we call non-linear design thinking. Non-linear design thinking is a method for re-framing design problems and spaces in a manner that avoids the errors in thinking that arise from assuming that relationships between design factors are linear when they are not. Our contribution is a framework for thinking about non-linear relationships in design and how to design taking these into account, illustrated with examples. This paper is a full-length extended version of the shorter nonarchival article  with added authors, examples, background, and details. About 40 percent of the material is new.