Basically you're asking for something like the 'Trust' system that was added to FFXI - which is really is as cool as it sounds. In that you can summon up to three copies of story npcs to help you in a battle, each one has their own unique skill and party role (tank, healer, melee dps, magic dps) and actually allow the player to effectively solo content that once required a party in the game, thus making it far easier to play now.

A version in FFXIV would probably require a lot of tinkering to get working properly though, given even our chocobo companion cannot be out when we queue for a dungeon, due to it mucking up the Duty Finder, so I don't hold out much hope seeing such a system implemented in FFXIV. It would still be awesome to have though.