What happens when a magnet is dropped through a solenoid with a current running through it?

I know when a magnet is dropped through a copper tube or a copper solenoid it induces a current in the copper and the magnet actually slows down as it falls through the tube, but if I did this with a solenoid that has current flowing through it, what would happen? Would there be some kind of interference since there is already a current but as the magnet falls it's supposed to induce one as well? I'm trying to design an experiment but I'm not sure if this is something that can be investigated or if the current/magnetic field simply cancels out if you do this.