Has anyone pursued two very different business ideas simultaneously? What was the outcome?

Mark Zuckerberg pursued TheFacebook and Wirehog simultaneously.

I can do u one better. Elon Musk has Tesla, SpaceX, and Solar City. So if legendary and fucking awesome is in your description go do it.

Very few people have the mental capacity to commit to more than one full-time start-up and do them justice. When I've seen it tried, the most likely outcome is the founder moving back and forth from one to the other depending on which is on an upswing at the time, and leaving the other to languish until the current upswing starts to peter out. It also gets pretty unnerving if either of those endeavors have employees.

Jack Dorsey square and twitter.

Distraction, especially at the start, is usually a bad idea. Focus is always a good idea.

Currently doing it now. Its taxing, but can be done if your teams are segmented appropriately. Our developers are, but our designer is designing for both (and hopefully not going insane for it). We came from an interactive agency background though, where almost any number of projects moving simultaneously was the norm. If you don't have that background, deep understanding in both startups, and a pro team for each, its going to be hard. We also have guys pushing each business forward in sales, so that's not all on me. If you're a one-man show right now, I'd have to advise you to pick one and run it down.