I looked in my Birds of Argentina book and got the following families completed for Argentina:
Rheidae, Podicipedidae, Anhingidae, Ciconiidae, Threskiornithidae, Phoenicopteridae, Anhimidae, Cathartidae, Phasianidae, Aramidae, Heliornithidae, Cariamidae, Jacanidae, Rostratulidae, Haematopodidae, Recurvirostridae, Chionididae, Tytonidae, Trogonidae, Momotidae, Ramphastidae, Bucconidae, Dendrocolaptidae, Phytotomidae, Corvidae, Cinclidae, Troglodytidae, Mimidae, Sylviidae (Polioptilidae), Vireonidae, Tersinidae, Ploceidae, Sturnidae.