Many codes now call for steps to meet the 17" or 18" rule, which is that the rise and tread add up to that figure. Ideal would be something like 7" rise and 11" tread. You could get a piece of 2x the next size larger than now used for the stringers. That might be a 2x12 nominal. Then lay out the new steps on that using the existing stringer as a guide. Remember that all rises must be the same including the steps themselves.
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