Shin Megami Tensei: Persona 3: FES is an "enhanced" version, much like a Metal Gear Solid Subsistence version but with more content, more events and a new quest -- and for only $29.99, no less.
It's a role playing game and a mash up that includes the familiar party-based or group based game, but one that also incorporates the relationship/dating genre.
You begin the game as a student who leads a secret life, one in which you have the ability to use and collect Persona, a creature that's equivalent to magic. These creatures have awkwardly named spells/attacks, but they function much like Summons in Final Fantasy, with a nod toward Dragon Quest's sense of humor.
During the day, you live the student's life and must navigate through class and exams, all the while developing and building relationships within the various locales on the map. Building these relationships increases your Social Link, which enables you to create stronger versions of Personas when combining them. For instance, if you could already create a new Persona by combining two others, the right Social Link might let you get a bonus that raised the Persona a couple of levels.
Every night at midnight, though, is the shadow's realm, and it's from here that you'll grind out your levels by tackling various enemies and bosses. In a nice touch, enemies aren't random, and in fact they're completely visible, so you can attack them unawares for an instant advantage in battle. There is one random element, however: a random dungeon generator that goes through a series of "floors" rather than levels.
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I might just wait for the first Persona that comes out on the PS3 though....