This will be really hard to explain with my skeleton (which is WAY more complex), but I've tried to boil down the problem into a very simple example that illustrates the same issues.

Imagine that this is a character in a top-down, isometric perspective. So the camera is not a side view, but slightly above (think Final Fantasy Tactics, Zelda, etc). My character here is facing Southeast. The eye and mouth are the character's actual eye and mouth, and those are children of a head bone (in gray). The other two green arrow bones are the bones to which I would attach their torso and legs, etc. which are children of the main character spine (also in gray).
Below the skeleton, I have a bone (Character Heading - the one that's currently selected) that controls the character's facing direction. I have transform-constrained the angle of all the green body part bones to this Heading bone (set to 100%).
In the game, we will programmatically change the angle of the orange Character Heading bone as the character faces different directions, plus swapping textures, etc - don't worry about the details of how the character's textures would be changed to face those directions, since that's another issue entirely.
So when the orange Heading bone rotates, the eyes and mouth will rotate to follow it:

This works perfectly.
However, if I want to tilt the character's head slightly to one side (let's say they are aiming down the barrel of a gun, cocking their head, or some other body motion like that)... then we run into issues:

As you see, since the eye and mouth are inheriting their rotation verbatim from the Heading bone, they do not rotate with the head. Rather than the eye still looking like it's positioned above the mouth (with respect to the entire head), they are now side-by-side, and my character looks even more like a mutant 🙂 There are all kinds of ways that I could correct this issue, but I would really like a more direct solution:
Allowing constraint transforms to be additive.
If the angle of the eye and mouth could be both inherited from their parent (the head bone) and added to the rotation of the Heading bone, then they would appear as desired, here:
(this is just an approximation, the angle probably isn't exactly correct since I did it by hand rather than mathematically):

*one correction - my constraint called "head angle constraint" should have been called "eye angle constraint". Sorry for any confusion there - the head bone (in gray) is not constrained to anything.