Hi Chipp - sweep does not really expect for a piece of the sweep to pivot around a single side point like the corner areas in your profile curve will require.
If you zoom in on the those "pole" corner areas you will probably see that the surface is likely a little weird and maybe has little zig-zags or wobbles in it.
Sweep is only really expecting to make segments where the surface does not bunch up on itself on the sides like that. So you can't really use sweep to do that quite in that way.
Probably the best way to get the result you want is to make a solid box to start with and then select these edges of the box and do a fillet:
Usually those kinds of partial sphere corner type areas should be done by filleting.
- Michael
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