Two-dimensional II-VI semiconductor nanoplatelets (NPLs) present exceptionally narrow optical features due to their thickness defined at the atomic scale. Because thickness drives the band-edge energy, its control is of paramount importance. Here, we demonstrate that native carboxylate ligands can be replaced by halides that partially dissolve cadmium chalcogenide NPLs at the edges. The released monomers then recrystallize on the wide top and bottom facets, leading to an increase in NPL thickness. This dissolution/recrystallization method is used to increase NPL thickness to 9 ML while using 3 ML NPLs as the starting material. We also demonstrate that this method is not limited to CdSe and can be extended to CdS and CdTe to grow thick NPLs. When the metal halide precursor is introduced with a chalcogenide precursor on the NPLs, CdSe/CdSe, CdTe/CdTe, and CdSe/CdTe core/shell homo- and heterostructures are achieved. Finally, when an incomplete layer is grown, NPLs with steps are synthesized. These stress-free homostructures are comparable to type I heterostructures, leading to recombination of the exciton in the thicker area of the NPLs. Following the growth of core/crown and core/shell NPLs, it affords a new degree of freedom for the growth of structured NPLs with designed band engineering, which has so far been only achievable for heteromaterial nanostructures.