your stance should remain the same width regardless of the type of squat, because that stance should be the one that allows the greatest balance between depth and force generation capacity, so there's no reason your foot position should vary based on where your arms are.
typically when people widen their stance it's because it feels more stable in an otherwise unstable feeling position. it also creates some hip impingment and makes a higher bottom point feel full depth. these things of course make the squatter able to move more weight initially (consider the typical powerlifting squat stance), but ultimately, these things are problematic.
experiment with varying widths and toe positions. ultimately you want to find the perfect stance for yourself and one that you can hit everytime, whether you're back squatting, catching a clean, or overhead squatting. it should all be the same stance.