Morphological control of nanocrystals has become increasingly important, as many of their physical and chemical properties are highly shape dependent. Nanocrystal shape control for both single- and multiple-material systems, however, remains empirical and challenging. New methods need to be explored for the rational synthetic design of heterostructures with controlled morphology. Overgrowth of a different material on well-faceted seeds, for example, allows for the use of the defined seed morphology to control nucleation and growth of the secondary structure. Here, we have used highly faceted cubic Pt seeds to direct the epitaxial overgrowth of a secondary metal. We demonstrate this concept with lattice-matched Pd to produce conformal shape-controlled core-shell particles, and then extend it to lattice-mismatched Au to give anisotropic growth. Seeding with faceted nanocrystals may have significant potential towards the development of shape-controlled heterostructures with defined interfaces.