It depends on building regs, give your local council building control a call.
Stairs can be a nightmare, I sed to live in Slough and had loads of hassle when I wanted to change the way the stairs ran.
As long as those small areas are level and the wood is glued/pinned down.
You might have a problem if the boards are bevelled though. And if the step(s) are tapered you end up with a lot of saw-waste
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