I ran on an 11 runner team (and ran 4 legs). It was *different * because you were "off-rotation" with everyone else, but otherwise it wasn't that bad.
First, recalculate all the distances figuring in that you must continue to run in order 1-10 three times, then have the first 6 people run a fourth leg. (e.g. the person who runs leg 1, would do his 4th leg at 31).
You'll have to try to put your fastest or strongest runners on legs 1-6 as they'll likely have to double (unless they get injured and you get to move up another person of the same gender).
With a mixed team, however, you ALSO have to figure out how to have women run at least 17 of the 36 legs (I think that's what the official rules say). So, theoretically, you'd be fine if you put 3 women in the first 6 legs, and saving the others for legs 7-10.
Get out the maps and calculator and figure it out before hand as it would be a nightmare to try to do it during the race. Also, be aware that you *won't* be switching vans at any of the "normal" places -- so 1) don't get lost 2) make plans to use those facilities -- food, showers, etc otherwise you will have to do without.
good luck -- and you'll get to feel really studly when you finish all 4 legs (of course, the macho Sunday morning run won't be possible ;-) )