You can install wood floors over existing wood floors, but it will add some thickness which may be an issue for transitions from other floor surfaces,as well as clearance at doors, jambs, cabinets, etc. For nail-down applications, use rosin paper between the floors and attach with fasteners recommended by the flooring company. Orient the new floor perpendicular to the old one if possible. For glue-down, you may have to sand the old floor to get good adhesion, or use a Luan subfloor nailed to the old floor.
One thing many people don’t think about is the transition from one flooring surface to another. Generally, the more flush you can get your floor surfaces, the better it will look, and the better the space will flow. So that may be a reason not to add flooring over other flooring.