I wouldn't be surprised if this specific idea has been brought up and discussed before but I do not ever recall seeing it. I, like I'm sure most of you on here enjoy the single-player experience that Bethesda creates for us in both Fallout and Elder Scrolls. I'd say that again, like most everyone here, I do not want Bethesda to focus heavily on a multi-player aspect of their game. However, they always consider it but it has yet to make it into any of their games. The reason being is that I'm sure it just doesn't work or feel quite right. However, with the incorporation of the Pip-Boy mobile app and the game (Fallout Shelter) it is clear that Bethesda is at the very least, re-thinking their strategies for their games. I would not be the least bit surprised to eventually see some kind of multi-player aspect in the Elder Scrolls or Fallout. And it got me thinking and I came up with what I feel would be the perfect way to incorporate multi-player while maintaining the integrity of their core, single-player game.
You should be able to invite a friend online to play along side of you as either one of the existing companions and/or a companion that they created that is customized to your friend's liking. The custom player would almost be a "mysterious stranger" type character who "randomly" shows up to help the protagonist carry out his or her quests. In this mode the main character would still have full control over what weapons he allows his now online companion to carry, what armor he or she has, etc. The only difference would essentially be that in place of an moronic computer companion you would now have an actual player. You could continue your story, do the main quests, etc.
Again, this may have been discussed before but I think it would be the best way to include multiplayer in Bethesda's open world experience.