Solver - Finding the next best solution

I have a spreadsheet set up where I have a number in cell S6 and I run solver to find the maximum value for S6, which is the best solution. I'd like to also find the 2nd best, 3rd best, 4th best, nth best solution. Right now to do this I added a constraint of S6<=T6 where T6 is S6 minus 0.001. I have to copy and paste the value of S6-0.001 into T6 because if I just put in "=S6-0.001" into T6 it will never find a solution of course. Then I hit solve and repeat the process. Is there a more efficient way to do this?