Why would any of the 3 sprites in the above example ever clip each other?
Its 3 separate sprites acting as one. If they're overlapping on horizontal scanlines, you are doing something wrong and everyone will notice it.
The bullets: You said you're flickering them. odd frames = 3 bullets. even frames = other 3 bullets. They're never on screen at the same time.
YEah, the bullets were correct. Look, I don't know WHY you'd want 2 or 3 sprites to ever overlap perfectly, but say, hypothetically, they did. Then my example would be correct, right?
I can think of one good reason to have a little overlap. Let's say it is a run n' gun where the character has a big gun. You want the legs and torso animated separately, but you want the gun to have 8 directions of independent movement. In that case, the torso and legs wouldn't overlap, but the gun could, at times, overlap both the legs and torso.
I do agree, though. I was diving too far into hypothetical territory and not addressing his practical request. So let me wax specific to try and make up for it. You'd have 3 16-pixel bullets in any given frame, 32 pixels of torso (or however wide the torso sprite is, maybe only 16), and then 32 pixels of gun sprite (which appears to overlap the torso sprite). In that case you'd have 7 slots in use, or 112 pixels of your total 256 available. If the torso is only 16 wide, that's 6 slots in use or 96 pixels.
Overlapping of sprites is where the bench analogy breaks down a little. If one guy sits in another guy's lap, he still uses up an extra spot on the bench.