There are building code requirements for stairs (tread depth and riser height) and they are pretty much universal over the country. Occasionally older homes have non compliant staircases, however, it should be relatively easy to build a new staircase over the old one (especially if the existing steps are concrete). Standard pre-cut dimensional lumber for riser supports (stringers) and treads are available at most building supply companies (like Lowes), and aren't expensive, all you have to do is modify the stringers to overlay the existing stairs, attach them with concrete anchors or other appropriate fasteners, and then build the rest of the staircase on top of the supports.....I've done a couple of times, and it is fairly simple with a few common tools.
Precut stringers:
Modify the underside of these to fit on top of the existing steps.......
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