Should I undercoat over old paint?

Whether you should undercoat over old paint depends on condition of old paint and type of undercoating. For house painting, you can undercoat or prime over old paint if old paint is in good condition, clean, not peeling, and you are changing color drastically, covering stains, or going from glossy to flat, as undercoat improves adhesion and coverage, but if old paint is failing, peeling, chalky, or greasy, you must scrape, sand, and clean first, not just undercoat over failing paint, otherwise new coats will peel. For previously painted walls in good condition, one coat undercoat then two topcoats gives best finish. For car underbody rust protection, you should not undercoat over old paint or old undercoating that is peeling, cracked, or rusted underneath, as new undercoating will trap moisture and rust underneath and worsen corrosion. You should remove loose old undercoating, remove loose rust, treat rust with converter, clean, and then apply new undercoating for good adhesion. If old undercoating is intact and well adhered, you can apply new coating over it after cleaning. So yes you can undercoat over old paint if old paint is sound and well adhered, but not over failing, peeling, or rusty old paint without proper prep and rust treatment.