Level 10, you unlock your next job ability. Level 15, you get the ability to morph into another type of the monster you're playing (Lizard to Snow lizard, with Snowball instead of Fireball. Mandy to Korrigan.)
At 15, you also unlock a ton of black magic spells, with Stone-Fire, Stonega, Poison, Bio, Drain, Blind, Blaze Spikes, Bind. Level 16, I got shock.
You can unlock new monster types for 3000 infamy (Raptor, Treant, Sheep, Beetle) You can get the Instincts for between 500 and 10,000 infamy. The cointeach on the far right has a quest, and the first quest asks which cointeach roams N Sandoria. I got it wrong, and he said I had to wait until the next day. (My guess is JP midnight, game day didn't seem to change anything.)
Level 17, you get warp, and blizzard!
If you get low on HP, stand still for a bit, and you get all your HP back. Didn't see it happen, I was typing up this post. Assuming it's similar to normal monster methods of getting HP when they go idle.
18, you get rasp. 19, you get Waterga!
20, you get your third ability. I got Brain Crush on a lizard (Ice), Mandragora you get Photosynthesis.
You get Ice Spikes, Choke, and Sleep.
This looks familiar.
Safe to assume, it's the Black Mage magic list.