Ultrathin metal films supported on transition-metal (TM) surfaces have been considered as promising catalysts due to the possibility to tune their chemical activity by controlling substrate strain, composition, and ligand effects, however, our atomistic understanding of the atomic structure of those systems is far from satisfactory due to the complex role of strain effects and adsorbed species. In this work, we will report a density functional theory investigation of the atomic structure of Pt overlayer, skin of PtAu alloy, and Pt submonolayer supported on the Au(111) and Au(332) surfaces, as well as the effects induced on the atomic structure by CO adsorption. For uncovered CO surfaces, we found the same trend for both Au substrates, i.e., there is a strong Pt preference for submonolayer sites, which is consistent with experimental findings and segregation energy calculations, however, the adsorption of CO molecules on the surfaces favors the location of the Pt atoms on the topmost surface layer due to the strong binding of CO molecules to the Pt atoms. For Pt/Au/Au(332), which is a high energy configuration, we found that the Pt overlayer adopts a Pt(111)-like structure instead of the expected Pt(332) overlayer following the Au(332) stacking, however, the steps are preserved once part of the Pt atoms are exchanged by substrate Au atoms or once CO molecules are adsorbed on the Pt overlayer, i.e., CO/Pt/Au/Au(332). Therefore, the atomic structure of Pt overlayer on flat and stepped Au surfaces under a CO atmosphere is complex due to the competing effects that favors different locations for the Pt atoms, i.e., segregation energy favors subsurface sites, while strong CO-Pt binding energy favors the formation of overlayers on the topmost surface layers.