Other than monospecific families, I don't believe I've completed any family-level taxa, but there are a handful of non-monospecific genera I have completed, such as:
Strepera (currawongs) - 3 species, all wild
Phylidonyris (a genus of honeyeaters) - 3 species, all wild
Monotaxis (a genus of emperor breams) - 2 species, both wild
Realised I'd forgotten some taxa here - I've also completed:
Cheloniinae (2 species, one wild one captive)
Paradisichthyinae (2 species, one wild one captive)
Schuettea (2 species, one wild one captive - this genus likely will be given it's own monotypic family in future)
Achoerodus (2 species, both captive)
Microcanthus (2 species, one wild one captive)
All 3 currently accepted species in the
Pseudanthias squamipinnis complex (3 species, 1 wild 2 captive - although some recognise a 4th species in this complex which I have not seen)
Trachinops (4 species, 2 wild 2 captive)
Chrysolophus (2 species, both captive)
Spilopelia (2 species, both wild)
Both subspecies of the Crested Pigeon
Ocyphaps lophotes (2 ssp, both wild)
All subspecies of the Galah
Eolophus roseicapilla (3 ssp, all wild)
Both subspecies of the Masked Lapwing
Vanellus miles (2 ssp, both wild)
Both subspecies of the Pacific Gull
Larus pacificus (2 ssp, both wild)
Both subspecies of the Wedge-tailed Eagle
Aquila audax (2 ssp, both wild)
Zanda (3 species, 1 wild 2 captive)
Calyptorhynchus (2 species, 1 wild 1 captive)
Polytelis (3 species, 1 wild 2 captive)
Both subspecies of the Pale-headed Rosella
Platycercus adscitus (2 ssp, both wild)
Both subspecies of the Western Rosella
Platycercus icterotus (2 ssp, 1 wild 1 captive)
All subspecies of the Noisy Miner
Manorina melanocephala (3 or 4 ssp depending on which taxonomic source you use, all wild regardless of how many ssp are recognised)
Both subspecies of Eastern Whipbird
Psephodes olivaceus (2 ssp, 1 wild 1 captive)
Both subspecies of Australian Raven
Corvus coronoides (2 ssp, both wild)
Both subspecies of Welcome Swallow
Hirundo neoxena (2 ssp, both wild)