mis-read your question

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You want to allow the stair tread to overhang or cantilever the outside riser by 2-feet, and the total stair width is 8-feet supported by 3 stringers. My mistake.

I would limit any overhang to less than 8-inches. I have never run across the use of this construction method, but a 2-foot cantilever, assuming unsupported 2x softwood lumber laid horizontally could easily break under forseeable loads, such as a person jumping down or landing hard on the outside of the overhang. 2x lumber is not generally rated for unsupported loads in the horizontal plane. Also, the wood will weaken over time, and failure would not be predictible. I have nothing to support this, but common sense suggests your proposal is risky. I suspect that if I securely clamped a piece of 2x lumber on a fulcrum, and jumped on the unsupported 2-foot extension, I could easily break it.

The longer the cantilever the higher the leverage on the board under load. If I happen to find anything on the breaking strength of 2x lumber in horizontal plane I will post back, but lots of variable here. I guess thats why you don't see it.