Epitaxial films of Sm0.4Y2.6Ga1.2Fe3.8O12have been grown under carefully controlled and essentially identical conditions on Gd3Ga5O12substrates cut in four different orientations: {112}, {111}, {110}, and {100}. It is found that the two‐parameter model for growth‐induced anisotropy is inadequate to describe the anisotropies experimentally determined from this group of films. In the context of the preferential site occupation mechanism for growth‐induced anisotropy, these results indicate that the site‐preference factors for the yttrium and samarium ions depend on the orientations of the growth faces in a more complicated way than has heretofore been considered.