Animal shelter officials said the male goat was found Tuesday. He was feverish and suffering from pneumonia.
He has joined the other two goats, nicknamed Duncan and Isadora, at the Farm Sanctuary in Watkins Glen, N.Y.
Officials say the goats' origin remains a mystery.
Animal Care and Control spokesman Richard Gentles speculated that they could have escaped from someone's backyard, a farm or market where they would have been slaughtered for meat.