With a slight change in spelling, you can.
And then you bring in the Hippogriff. Equileo? But no, the hippogriff has horse parts instead of lion parts. Falcoequus?
And where would Pegasus fit into this?
…and I think of this one:
Anyway, in response to the original question,
Wouldn’t the Roc be fairly straightforward? Accipitriformes, possibly related to the teratorn, which would put them in the Teratornithidae.