Yes, some lamps work with a twin filiament. a Low and med power one, both on together mean high power.
More commonly, if its a low voltage (ie. 12v) lamp, the base will be heavy as it contains a transformer.
If the lamp is a 12v lamp then the switch may chose a 4v for low, 7v for medium and a 12v tap for full power.
Others have a dimmer circuit which uses Triac control, you will have either a continuos dimmer or some fixed steps.
By the sounds of it your lamp is a bi-filiamnt type. I think perhaps the switch contacts have became dammaged and are messed about.
A new switch may be in order but a new lamp may be safet depening on your electrical skills.
Stuart.