After working through trying to do a mode change in same direction with Charlie's 9-square theory, I came up with an interesting solution that involves using soft transitions across a unit circle grid to switch between box and diamond mode. The idea for this is centered on isopops from hooping and more specifically how you can change circle size by treating them as adjacent circles rather than dilations of the same circle. Included is a demo of how this technique can be used to switch between iso vs cateye antibrid to static vs triquetra antibrid to iso vs extension and back again. I'm sure some others have played with this same idea, so I'd love to see what folks have cooked up.
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