You could argue that the Morpher class in FFTA was kind of a shapeshifter. It took the souls of monsters and used them to channel the attacks of the monster. Now all you would have to do is add in it actually changing forms and you have a legit morpher!

I can't think of anything totally original, but just some ideas:

Necromancer?- I can't recall it being in any other Final Fantasy. Hell...Lets just be honest, I just want a pet class
Spellblade- While not original, I can only remember it being in FFTA2 (And perhaps FF9 if you want to count the Steiner-Vivi combo). It would attack with mostly status inducing sword attacks. Think melee debuffer.
Wyrmtamer- Since Dragoon is likely not to have a pet, I think a pet class dedicated to solely dragon types would be interesting, and cause controvery with the lore, which, could be interesting. And I want a pet class.

That's...all I got.

(I claim this thread in the name of the return of Puppetmaster too)