What can I do about this deteriorating staircase?
Sure - many people build new wooden or "plastic-decking not-wooden" stairs over old, excessively steep concrete steps like that rather than rebuild the concrete ones, as much to make them more reasonable in rise/run and landing area as for fixing the basic steps.

In many ways it is easier if you demo the concrete ones first, (other than the concrete demo), since then you don't have to futz with supporting the pressure-treated wooden step framing on the old concrete steps. But plenty are done with the concrete steps still there below them.