How to depth test in one pass, then modify vertices in second pass?

I'm trying to render billboards at each vertex on a mesh, where if the center point of the billboard is occluded then the entire billboard is also hidden, and vice-versa (if the center point is visible, then the entire sprite is also visible).

Where I'm at currently:



Notice that the billboards are partially culled. Since I pass vertices as sets of 4 points all at the center of a billboard then transform them in the vertex shader, my thinking is...

How to depth test in one pass, then modify vertices in second pass?