Ksp value doesn't change, just less solid will dissolve since there are already dissolved particles present, and the solution can handle only so much.
For example, if you're trying to dissolve of NaCl in a 1M solution of Na+, Ksp will always = [Na+][Cl-] Since you already have 1M Na+, the equation will look like Ksp = [1 + x][x] ....just solve for x and that's your solubility.
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