A mad geneticist! Collect bio data from slain enemies and forge your own monster to fight for you in battle! DevilCrab with a DinoZombie head? You can do that! Gloom Widow and Little Chariot? Mecha Death Spider! Movers and a Grenade? Self-replicating explosive! Where do the possibilities for your sin against nature end?!!

But seriously, the idea seems like it could be a lot of fun. Give the player a command similar to Catch, and allow them to elect to keep a monster's color palette, head, body, or ability, and let them run with it. From certain body parts the monster would inherit certain traits, such as floating status for winged bodies and elemental strengths and weaknesses from a bomb's face, and abilities/commands could be gained similarly. Instead of using equipment, the creature's stats would be determined by adding the modifiers from certain body parts and abilities to the player's base stats. Additionally, specific combinations could even create special, hidden monsters for the player to control, like the aforementioned Gloom Widow + Little Chariot combo giving a mini X-ATM; there's no reason specific abilities/attacks couldn't combine in a similar manner as well.

Of course, there would have to be serious tradeoffs to balance out the class, so the monsters would have to be weaker than most other job classes to make up for their 'free' customization, and the player would have to play on their adaptability with a creative mind to make up for that.