This paper presents a novel family of modular flat-foldable rigid plate structures composed by assemblies of 4R-linkages. First, in the field of foldable plates, the proposed system is characterized by being not only foldable but also transformable: the slope of one module over the other is capable of changing not only magnitude but also sign. This transformable behavior extends the range of application of foldable plates from simply larger-smaller configurations to substantially different configurations and usages. The transformable curve is obtained by means of symmetry operations on the spherical length of links. For each module, three configurations can be designed. Various examples are illustrated.