Hi Oliva, Great question!
Staircase corries are also known as staircase cirques, this is when there are more than two cirques, where one is sat above another.
Staircase cirques form with the same process as a stand alone cirque, beginning with a small hollow which overtime expands due to both physical and chemical weathering. You can learn more about cirque formation here. This means that if there are a series of hollows in a suitable valley, over time staircase cirques may form.
I hope this helps!