We have been able to grow well-ordered crystalline overlayers of either alkylthiols or dodecane on the surface of self-assembled monolayers (SAMs) of alkylthiols on Au(111) by exposing the surface of a preexisting SAM to the appropriate amount of flux at carefully controlled temperatures. Low-energy helium diffraction shows that, with one notable exception, all overlayers proved considerably more ordered than the underlying SAM. Debye-Waller measurements also reveal that the overlayer surfaces are stiffer than the underlying SAM surfaces that support them. Dodecane overlayers have the same structure whether grown atop SAMs made of alkylthiols containing either 10 or 11 carbon atoms. However, the overlayers of C10SH on a C10SH SAM surface were distinctly different from and of higher quality than the overlayers of C11SH on a C11SH SAM surface. To the best of our knowledge, this is the first structural characterization of an organic monolayer grown on an organic substrate of a different structure.