What about a mimic class?
The Mime.

Would just like Gau+Gogo in FFVI (FF3 US), you morph/act as a monster and get all of his moves scaled to your level and stats. Also, you get the ability to "mimic" any last action of any PC/NPC/monster you target.

As you level up, you earn monster "profiles" with expended move sets when you morph/act as this monster (instead of earning actual abilities, you earn profiles for more abilities when morphed/acting as a monster).

Ex.: Level 1, profile Rat (Instead of getting only 2~3 abilities from copying a specific Rat, you get more abilities from all the "squirrel/rat" in Eorzea).

It is different from Blue Magic in the sense you do you copy only 1 move but the entire set of a monster. You are also limited to those copied abilities + free class abilities.

What would be the job of the Mime? Blue Mage, obviously!
You get rid of the inconvenience of not being able to equip other monsters abilities, but you get less abilities from a copied monster.

Just a thought, it obviously need adjustments and I'm sure the devs and community will happily comment on this.