Method accepting two different types as parameter

How about this:

interface ICrushable {
    void crush();
}

utterlyDestroy(ICrushable parameter) {
    // Very long crushing process goes here
    parameter.crush()
}

utterlyDestroy(Dreams parameter) {
    utterlyDestroy(new ICrushable() { crush() {parameter.crush();});
}

utterlyDestroy(Garlic parameter) {
    utterlyDestroy(new ICrushable() { crush() {parameter.crush();});
}

New development should implement the ICrushable interface, but for the existing Classes, the parameter is wrapped in an ICrushable and passed to the utterlyDestroy(ICrushable) that does all the work.