Dual doping is a powerful way to tailor the properties of semiconductor quantum dots (QDs) arising out of host-dopant and dopant-dopant interactions. Nevertheless, it has seldom been explored due to a variety of thermodynamic challenges, such as the differential bonding strength and diffusion constant within the host matrix that integrates with the host in dissimilar ways. This work discusses the challenges involved in administering them within the constraints of one host under similar conditions of temperature, time, and chemical parameters such as solubility and reactivity using CoPt-doped CdS QDs as a model system. In addition, the various forces in play, such as Kirkendall diffusion, solid- and liquid-state diffusion, hard acid soft base interaction with the host, and the effect of lattice strain due to lattice mismatch, are studied to understand the feasibility of the core to doped transformation. These findings suggest a potential approach for manipulating the properties of semiconductors by dual doping engineering.