Essentially, each character can gain social links with one another, and with a few of the NPC's I'll be introducing soon. Instead of powering up newly created Personae via fusion, I imagine they'd power up the one you have based on their arcana. Granted, in Persona 3 Portable, with the female protagonists route, Akihiko is of the Emperor arcana, but pursuing his social link levels up your Star Arcana. Likewise, Shinjiro is of the Hierophant Arcana, but pursuing his social link levels up your Moon Arcana. So it's not set in stone.
When it comes to Player Interactions, I'm going to let you handle it with each other, but you can only level up your social link once per interaction, or if you interact poorly, it might not level up at all. I may step in if necessary but I doubt I'll need to. Since there wasn't much support for it, we're NOT doing a numerical stats based system. Instead, we'll just roleplay that specific traits of your persona get stronger. For instance, let's say you level up your magician arcana, your persona will become stronger with magic, or be better able to resist it.