Z-Index on CSS 3D? Disable depth buffer?

Greetings!

I have a CSS 3D issue. We display text boxes and I would rather like them to overlap than intersect as can be seen in the uploaded picture. I do not want to alter the Z value of the Matrix, because this distorts the perspective. Is there any way of using Z-Index or perhaps layers to ensure, that the text boxes are drawn without intersecting with the depth buffer? I think this is more of an CSS issue than THREE JS.

AFAIK, this can’t be solved with CSS. Apart from using z-index, it’s not possible to influence depth testing like in WebGL.