The behavior of C-60 molecules deposited onto 11-phenoxyundecanethiol (phenoxy) self-assembled monolayers (SAMs) is studied using ultrahigh vacuum scanning tunneling microscopy (UHV-STM) and spectroscopy. We observe that after thermally annealing between 350 and 400 K in vacuum a combination of hexagonally close-packed islands, rectangularly packed islands, and isolated single lines of C-60 is observed when the C-60 is initially deposited on an unannealed phenoxy SAM. However, only rectangularly packed islands are found when they are deposited on a preannealed phenoxy SAM. We determine the rectangular packing to have a (2 root 3 x 4) rectangular unit cell with respect to the underlying Au(111) substrate. This type of C-60 structure has not been observed previously for multicomponent self-assemblies on a surface. We discuss the possible causes for the formation of this structure as well as the differences between starting on an unannealed SAM and an annealed one. This study demonstrates the capability of functionalized alkanethiol SAMs to control the growth and structure of C60 islands during annealing depending on the structural changes of the SAM itself; by preannealing the SAM, the motion of the C-60 can be confined and unique structures resulting from interactions between the SAM molecules and C-60 can be produced.