Al-Shafi‘i requires at least three cleansing wipes, whether using three separate stones or three clean edges of one stone.
His evidence is the Prophetic instruction:
فَلْيَسْتَنْجِ بِثَلَاثَةِ أَحْجَارٍ
Translation: Let him cleanse with three stones.
The imperative is understood to establish a minimum of three wipes, even where cleansing appears complete earlier.