Every overlay must have a unique Material Layer Key property. Otherwise, they will interfere with each other. In addition, if you need to have two clipping material layers, you’ll need to create a custom material that supports this.
You’ll need to copy the MI_CesiumThreeOverlaysAndClipping and duplicate the Clipping material layer. Give the new layer a different name, e.g. name one Clipping0 and the other Clipping1. Then set the Material Layer Key in each polygon overlay to match one of the material layer names.
You may want to delete some of the other layers you’re not using, like Overlay0,1, and 2, in order to make the material simpler.