For Lorentzian, as you shift the filters with respect to each other, it not only becomes dimmer, it also becomes wider. I tried to show it in the attached figures. The first shows (on an arbitrary frequency scale centered at 0) a single stack (SS) and double stack (DS center), the latter being the square of the first.
The second figure shows two SS's each offset in opposite directions but with the same bandwidth. The product is "DS shift," and "DS shift norm" is the same curve normalized to better see the width.
The third figure compares DS center to DS shift. The normalized version demonstrates that it gets wider.
As always, I could be wrong, but these were the kind of figures I was looking for. Sorry about the wrong function earlier.