If you wish to overprint the foil with ink, there are special foil formulations for this application as well as foiling over ink.
Foil stamping is truly a value-added process. The cost of adding a color with foil is, in many cases, less expensive than adding an additional color of ink. If your design is properly structured, you can stamp multiple colors of foil in a single pass, for great cost effectiveness. More importantly, the perceived image is greatly enhanced beyond normal expectations of inks – even metallic inks can’t equal the richness and saturation of color found in foils.