In study on drop-on-drop impacts, we derive the kinematic and dynamics conditions and regime map selecting for the Crescent-moon fragmentation regime important for impacts on surfaces of intermediate wetting. Using a combined geometric and momentum conservation argument, we also derive the expressions governing the base of the Crescent-moon and its pair of lateral ligaments. For more, read: Wang, Y. and Bourouiba, L. (2018) Non-isolated drop impacts. Journal of Fluid Mechanics. 835:24-44.