We present results of a scanning tunneling microscope (STM) study of Rh/Ag(100) epitaxy, which shows how the surface rearranges toward the more stable encapsulated structure known to form at higher temperatures. At room temperature, Rh growth proceeds via two competing pathways: (i) thermally activated exchange with Ag surface atoms, which leads to increased coordination of the higher surface free-energy metal Rh by Ag atoms, and (ii) nucleation and growth of mixed Rh/Ag adislands. The Ag-Rh interaction also reduces the surface mobility of Ag, e.g., by local pinning of step edges, accompanied by complex step and surface erosion processes.