The 33-year-old victim was found with devastating bite injuries after leaving the house.
Police said two dogs were seized in the Rubery area of Birmingham after Wednesday's incident.
They are now looking for two more American bulldog types, which are not thought to be a banned breed.
Insp Leanne Chapman, of the West Midlands Police dog unit, said they knew at least two were missing, but revealed there may possibly be a third.
Seized
West Mercia Police are assisting the hunt while drones were being used to scan the surrounding neighbourhood.
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