Since nothing else is specified... with perfect wire and voltage source you could in theory run additional giga-tera-peta-amperes through the switch and the bulb would still be as bright as before.
As long as the voltage across the bulb is constant, the current will also remain constant.
If you consider that real wires and batteries have a resistance greater than zero, then switching in the resistance will have some effect. It's still plain old Ohms law, except there now some additional resistance that previously wasn't accounted for.