As far as a standard RPG Maker game goes, I think there are a lot of asynchronous online features that would actually take away from the game experience, like item trading or allowing someone else to complete a puzzle for you. This kind of thing shatters the fourth wall of gameplay, allowing progress or power to come from sources completely exogenous to your own interaction with the game.
With that being said, friendly PvP combat between my party and another player's party would probably be my most wanted feature for such a game. Since you asked for what might be cool beyond PvP, I think it would be really cool, in the right game, to be able to influence certain things in the game world for everyone who I've connected to, by doing certain things in the game world. Perhaps a very difficult sidequest allowed a new building to be built somewhere in the world, or introduced a new item to a shop, for everyone I've connected to. Perhaps I killed off an unimportant NPC and now they're gone for everyone else I'm connected to. Or even much smaller things, like being able to leave messages in dungeons for other players I've connected to, or influence NPC dialogue.