Running Parallel Campaigns

So, as seems to frequently be the case with me, more players wish to be a part of my new campaign than I’m comfortable putting around one table (maybe 8). I toyed briefly with the idea of running two campaigns with different parties in parallel in exactly the same world (their actions can affect each other and the world in general, etc). I’m not likely to go down this route – it would require a substantially greater investment of time I don’t have – but it made me curious.

Has anyone ever run two campaigns in parallel? How did it go? What were the pitfalls you experienced, and how did you work around them? Were there any really cool moments that came about because of it? What special considerations would you make in planning such an undertaking?