Double-layer tensegrity grids (DLTG) are spatial reticulated systems based on tensegrity principles, which have been studied in detail over recent years. The most important investigations have been carried out focusing on a short list of tensegrity grids. This paper explains with real examples how to use Rot-Umbela Manipulations, a unique technique developed for generating innovative typologies of tensegrity structures. It is applied to two already existing tensegrity grids in order to obtain two new DLTGs. Their analysis permits us to identify, inside these novel grids, the modules that compose them which were unknown until now. A brief description of these components is provided, as well as some information about their static analysis, e.g. states of self-stress and internal mechanisms. These novel modules belong to a family, all of them with similar characteristics in terms of geometry and topology, and can be used to generate a wide catalogue of DLTGs. Some examples of new grids are presented, describing the methodology on how to obtain many more models for other designers interested in creating and studying innovative DLTGs.