We use Ca doping during growth of one- and two-monolayer-thick MgO films on Ag(100) to identify the adsorption sites of individual adatoms with scanning tunneling microscopy. For this we combine atomic resolution images of the bare MgO layer with images of the adsorbates and the substitutional Ca atoms taken at larger tip-sample distance. For Ho atoms, the adsorption sites depend on MgO thickness. On the monolayer, they are distributed on the O and bridge sites according to the abundance of those sites, 1/3 and 2/3, respectively. On the MgO bilayer, Ho atoms populate almost exclusively the O site. A third species adsorbed on Mg is predicted by density functional theory and can be created by atomic manipulation. Au atoms adsorb on the bridge sites for both MgO thicknesses, while Co and Fe atoms prefer the O sites, again for both thicknesses.