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The zinc blende (γ) phase of copper iodide holds the record hole conductivity for intrinsic transparent p-type semiconductors. In this work, we employ a high-throughput approach to systematically explore strategies for enhancing γ-CuI further by impurity incorporation. Our objectives are not only to find a practical approach to increase the hole conductivity in CuI thin films, but also to explore the possibility for ambivalent doping. In total 64 chemical elements were investigated as possible substitutionals on either the copper or the iodine site. All chalcogen elements were found to display acceptor character when substituting iodine, with sulfur and selenium significantly enhancing carrier concentrations produced by the native VCu defects under conditions most favorable for impurity incorporation. Furthermore, eight impurities suitable for n-type doping were discovered. Unfortunately, our work also reveals that donor doping is hindered by compensating native defects, making ambipolar doping unlikely. Finally, we investigated how the presence of impurities influences the optical properties. In the majority of the interesting cases, we found no deep states in the band-gap, showing that CuI remains transparent upon doping.