Suppose the response you already had was called Y1. You can just add more columns to the table for the new responses (say Y2 and Y3) using 'Cols > New Column...' and fill in the measured values. When you run the analysis scripts that JMP has saved in your table, you just have to then be sure that you also add Y2 and Y3 as response columns. By defining desirability functions, you can perform simultaneous optimisation after you have a model you like.
(I'm assuming here that you do indeed want to treat each response 'separately', and have no need to worry about any correlation structure they might have).