The main strategy for constructing porous solids from discrete organic molecules is crystal engineering, which involves forming regular crystalline arrays. Here, we present a chemical approach for desymmetrizing organic cages by dynamic covalent scrambling reactions. This leads to molecules with a distribution of shapes which cannot pack effectively and, hence, do not crystallize, creating porosity in the amorphous solid. The porous properties can be fine tuned by varying the ratio of reagents in the scrambling reaction, and this allows the preparation of materials with high gas selectivities. The molecular engineering of porous amorphous solids complements crystal engineering strategies and may have advantages in some applications, for example, in the compatibilization of functionalities that do not readily cocrystallize.