Clipping with 3 planes, stencils and clipIntersection=true

I have successfully integrated the stencil approach used in three.js/examples/webgl_clipping_stencil.html at ef80ac74e6716a50104a57d8add6c8a950bff8d7 · mrdoob/three.js · GitHub into my application.

The application allows to switch between clipIntersection = true or false. I fully understand why with clipIntersection = true the given stencil approach doesn’t work any more. However, I have no idea how to change the logic so that the clipped intersection areas get properly filled with the stencil based planes (think of the outer shell of three.js/examples/webgl_clipping_intersection.html at ef80ac74e6716a50104a57d8add6c8a950bff8d7 · mrdoob/three.js · GitHub, just not open, but the open areas properly capped at the clipping planes)

Does this work at all? And if so, does anybody know how that could be achieved?