In this study, we modify the flux-growth method for the purpose of exploratory synthesis of ternary intermetallic compounds. Our concept is based on the assumption that valence electron count plays a crucial role in the stability of polar intermetallic compounds of different structure types. Control of the valence electron count parameter is made possible through the use of an excess of two metals having a different number of valence electrons. By gradually changing the ratio between these metals in the joint flux, we scan the gross number of valence electrons and explore the crystallization of new compounds. In the ternary system Re-Ga-Zn, we detect compounds belonging to three structure types, ReGa5, PtHg4, and V8Ga41, while gradually increasing the content of Zn metal in the flux. Two new compounds, ReGa3Zn and Re8Ga41-xZnx with x = 21.2(5), are obtained in the form of high-quality single crystals, and the former compound shows the narrow-gap semiconducting behavior favorable for high thermoelectric performance.