Hi glmr, thanks for posting the file. For this case I'd recommend splitting the object into 2 pieces and using Edit > Trim to cut the pieces with each other.

I first used Edit > Separate to break the object into individual surfaces, then used Edit > Trim with the "Isocurve" option to split the self-intersecting surface into 2 pieces. Then I used Edit > Trim using those surfaces to cut each other, then Edit > Join afterwards. See the attached 3dm file for the result.

Booleans will be a little difficult in this case because the self-intersecting area has some little slivery pieces poking through:





- Michael