We study the role of the third metal oxide in In-Ga-Zn type oxides (IGZO), Ga2O3, by comparing the calculated electronic properties of various alternatives (Al, Y, Hf, Ti, Si, W) to Ga. It is found that Ga2O3 causes little disorder in the conduction band minimum (CBM) energy based on In or Zn oxides, and it has a large O vacancy suppression effect, which benefits both a high mobility and a low OFF-current of IGZO. However, other alternative choices give a pronounced conduction band disorder potential due to their higher CBM energies, and thus are not ideal components in amorphous oxide semiconductors. Si and W may reduce the negative bias illumination stress instability by lowering hydrogen induced states to below the bulk valence band maximum but Si is not beneficial for mobility. Their role in back-end-ofline transistors is also noted.