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Not used any myself, but was thinking along the lines of this?
https://industrialsuppliesco.co.uk/products/sound-proofing-and-deadening-rubber-sheet-linear-meter?variant=42370839806186¤cy=GBP&utm_medium=product_sync&utm_source=google&utm_content=sag_organic&utm_campaign=sag_organic&gclid=Cj0KCQjwpcOTBhCZARIsAEAYLuXLwdP9ssugIMqxJusbTs0X6_QEQPcIQdNcsKyXk9ZwOibqEo8p1DAaApfDEALw_wcBDid something similar with the back of the front door in an old flat, but using acoustic foam and it worked quick well to keep the noise from the stairwell out.
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Yeah it depends on what sort of noise it is.
If it's loud creaks that are happening when you walk up the stairs then you'll need to get in under the stairs.
The treads and risers are wedged into the stringers. Creaks can be caused by loose wedges that are allowing movement. Get under and check if any wedges are blatantly loose or missing.
can you acess the underside of the treads?
some kind of self-adhesive rubber stuck in there if so?