I have no imagination.
Oddly enough, asking for a new animal by combining three is a popular one in art classes. Or at least it was in the classes I remember. They didn't have to be pets, at least, but the idea was still to use real-life references with originality.
I hated that assignment.
The straight truth is that I don't have that kind of creativity. I've always preferred working with what's *there* already. I'm too practical for the fantastical and can't let go of "this wouldn't work"--the details just get me all tangled up.
But I do have a favorite tri-creature.
Diana Wynne Jones' book Dark Lord of Derkholm has griffins physically eagle and lion, but mentally the children of their *human* parents. (Their father is a magical cloner). So two of the children are human, but the rest (at first) are griffins of various colors and sizes and magical abilities.
Kit is my favorite. He's the first, the biggest, and the darkest. The book itself skews toward campy humor, and slightly satirical, and then it takes a darker turn--
I must like this style, I just realized its similarity in that way to the Rogue Agent series. --
Anyway, Kit is my favorite, but especially paired with his human brother, Blade. The two of them join up, with the rest of the family to help their father be the "Dark Lord" for a series of tours from a world like ours wherein the tourists pretend to be part of heroic groups. Of course, these themed battles really do destroy their world. And Kit and Blade learn magic (from a giant old dragon).
It's been so long since I read those two books. I need to read them again! I guess I don't dislike this prompt so much anymore.