Multi-stage ko
A multi-stage ko is a special ko fight, where taking the ko produces another ko mouth. This new ko can then be fought, and this may continue for several stages. A multi-stage ko is also known as an iterated ko, or dan ko in Japanese.
In a multi-stage ko, the fighting shifts from one ko mouth to another, so that when the original underdog takes the next ko, the opponent is taken one ko fight away from winning the whole ordeal. In a two stage ko that means that the opponent becomes the new underdog.
Contrast this with an approach ko, where all the fighting is done at the same ko mouth, and the best that can happen to the underdog is that the ko turns in to a direct one.
For examples and more explanation, see two stage ko and three stage ko.