Garbz
No longer a newbie, moving up!
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I would strongly recommend against doing that. That is no fewer than EIGHT air to glass surfaces, and if the CP are uncoated or single coated, you are setting yourself up for flare and or ghosts. Not to mention light loss and therefore an effective smaller maximum aperture. Not to mention that you will also get some weird color saturation and rendition.
Part of what creates additional flare relies on a change in angle of the light between refractive surfaces. For most filters this appears as two additional flares each on opposite sides of the light source. While you're right that a CPL filter has 4 air to glass interfaces, two of them are not field relevant due to how close together they are. You would see no additional flare as a result of this.
Stacking CPLs on the other hand would still double the amount of flare compared to a single one, but it's no where near as bad as your bold italic and capitalised word makes it out to be.
May I also mention that light loss is the entire point of this exercise.