I don't know a way to actually copy the view but it is possible to have two identical detail views. Start by making sketch of the detail shape you want. Then create another sketch of the exact same so that all lines are constrained to be the same as one another. After this create a detail view selecting one instance of the closed profile. After that create a detail selecting the 2nd set of lines. Turning on selection filter for "sketch segments" helps so you don't accidentally click the created detail. The profiles should overlap each other now so it will look like one detail. Although at this point you will want to delete the Detail name off of one of them and copy the annotation from one to the other.
Not the best solution but it should give the desired result. Hope this helps!
Another option would be to insert another drawing view of the model, set it to the same scale as the detail view, and crop it to match the detail view.
Yes, I agree with Glenn - I often need to put model views outside of the paper borders so I can create sections or details from them. Later I can hide the view if I want (without hiding the derived views). On larger drawings this does have the downside of increasing file size.