Is it possible to have a reverse fold in a flat die cut corrugated cardboard box insert?

I'm designing a box insert from C-flute corrugated cardboard. I want to make a suspended sunken platform and the design I have come up with requires 2 normal folds and 2 reverse folds. The firm doing the die cutting tell me that folds can only go one way when using flat die cutting machinery. This totally screws up my design so i'm wondering if a reverse fold can be made anyway or if there is a way to cut the board such that a reverse fold is enabled. e.g. cutting each end of the fold line, aligning the fold line parrallel to the corrugations or punching slots through the fold line.

Answers:
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