Colloidal semiconductor nanoplatelets (NPLs) have been known to exhibit favorable optical characteristics, such as a narrow emission bandwidth, giant oscillator strength, suppressed Auger recombination, and polarized emission, which can merit their use in light-emitting diodes and lasing devices. However, to date, NPLs have shown a relatively limited range of emission energy because of their thickness-dependent discrete band gap and restricted choice of chemical composition (mostly CdSe-based), impeding the realization of R, G, and B full color display based on NPLs. CdSe-based core/shell NPLs can only cover the emission range from yellowish green (similar to 550 nm) to red (similar to 620 nm). In this study, we synthesize CdZnSe/ZnS core/shell NPLs with significantly enhanced spectral tunability over a broad spectral range (425-570 nm). Particularly, to overcome the difficulty in the synthesis of composition-controlled CdZnSe NPLs, we carried out a Cd-to-Zn direct cation exchange reaction on CdSe/ZnS core/shell NPLs using ZnI2 and an oleylamine (or trioctylphosphine oxide) ligand, which allows for the composition change in NPL emitting core while maintaining the original shape of NPLs. With the control of the reaction temperature and time as well as the ligands, the exchange reaction enables us to demonstrate an unprecedentedly wide emission range and spectral tunability of NPLs with the emission wavelength reaching 425 nm. Furthermore, as the core alloying proceeds, NPLs maintain excellent color purity and exhibit linearly polarized emission. Our light-emitting devices using the cation-exchanged CdZnSe/ZnS NPLs hinted at the possibility of using the NPLs in full-color display applications. Based on the elemental mapping analysis and experimental results, we proposed the temperature-dependent cation exchange reaction process in core/shell NPLs.