CONSPECTUS: Crystal engineering is the art and science of making crystals by design. Crystallization is inherently a purifying phenomenon. Bringing together more than one organic compound into the same crystal always needs deliberate action. Cocrystals are important because they offer a route to the controlled modulation of crystal properties. The route to cocrystal synthesis was opened up with the heterosynthon concept, which considers the complementary recognition of chemical groups from different molecules. Using this concept, binary cocrystals of enormous variety have been generated, even as crystal engineering has evolved into a form of solid-state supramolecular synthesis. Introducing a third component (a component is somewhat arbitrarily defined as an organic substance that is a solid at room temperature, mostly with the idea of excluding solvates) in a stoichiometric manner requires substantially greater effort and a careful balance of intermolecular interactionstheir strengths, directional properties, and distance falloff characteristics. The first systematic ternary cocrystal synthesis was reported around 15 years ago. Drawing in a fourth component in stoichiometric amounts is exceedingly difficult, and we reported such syntheses in 2016. To date, a limited number of ternary cocrystals have been realized (around 120 in all, with a half from our group) and an even smaller number of quaternary cocrystals (around 30, all from our group, barring one). It is impressive that our experiments largely yielded the intended higher cocrystal (three-or four-component) with very small traces of contaminating binaries and pure compounds. A fifth or sixth component may be brought into the solid in the manner of a solid solution in that these components are situated at one of the sites of the quaternary cocrystal. To date, five components have not been included stoichiometrically within the same crystal. This is still an open challenge. The merit in synthesizing (higher) cocrystals is that one can systematically engineer property modularity: Each component is associated with a distinct property. This is important in the pharmaceutical industry, where each component can, in principle, confer a different, desirable propertydrug action, solubility, or permeability. However, difficult synthetic targets are also addressed in chemistry simply because they are there. The intellectual satisfaction in making something that is very difficult to make renders the enterprise worthwhile in itself, and new chemistry usually gets uncovered in the process. The development of synthetic organic chemistry can undoubtedly be credited to various reliable methods for chemical transformations, and many difficult total syntheses were achieved by employing these methods over two centuries of research. In contrast, supramolecular synthesis (of multicomponent cocrystals and other assemblies) is in no way at a similar level of sophistication because the subject is still relatively young. Our group and others have reported the synthesis of many hi...