Red Oak in Minnesota runs dual tees with 10 baskets. Very well done and one of the best courses I have played in the area. Even when the difference between the two pads are only a few feet, it feels like a completely different shot.
Hole 1 is slight uphill through a tightish fairway with a few smaller trees in the middle. Assuming I stay clean of those trees in the middle as it slopes uphill, I can run the basket with a FD.
Hole 11 is about 20 or so feet further back, maybe 30, but not further than that. That room for error suddenly seems harder to hit, as is any window or tunnel a far ways down the fairway. It took one of my most beautiful shots ever to run the basket with a DDX, otherwise, I am content with getting close and just taking a three, whereas from Hole 1 I know I can be within range of a birdie considerably more often.
Overall, a wonderful use of elevation and the trees. Numerous "sharing" tee pads are less than one hundred feet a part but totally change the whole dynamic of the hole.
It sounds like Red Oak is the exception, not the rule of multiple tee pad courses.
I have property up-north where I have contemplated carving out some holes to play and plopping down my portable baskets. It seemed the more natural thing to do to increase the playability and reducing the monotony of it to make several tees and fairways leading up to a few central baskets. I only have four portables to work with, and I would rather not have to lug them around from fairway to fairway.
Of course this seems like a more viable option considering my situation, but when it is a permanent course, as demonstrated by Red Oak, it can be done correctly as well and should make it be considered a 20 hole course, not 10.
Yet, just to bring another Minnesota course into discussion, Lochness is a nine hole course with three sets of tees on every hole. In most cases, they are just extending the shot and not reshaping the flow of the fairway. The deal here, however, is that most holes from the shorts are already pushing par 4s to par 5s; the longs do not really change those pars, but just reduces the likelihood of getting that lower range as often. I would never consider this a 27 hole course.
I think it really comes down to is whether you are feeling inclined that it is a must to play through again from those other tees. Red Oak, yes, you almost have to. Lochness, no, once you are done with 9, you are likely done because you would not see anything new by playing another round.