Solution/altenative To Data Table Using >2 Variables

Is there a way to test out a formula using Excel that has more than 2 variables? (If only 2 variables, I would use a simple data table). The formula I am testing has 50X50X20 variables (and as a subset, each variable has 2500 lines of assumptions!). I don't need to see all the results, only the result that produces the highest result. For simplicity (if someone has an answer) let's assume 3 variables are A1, A2 and A3. Formula is in A4 and formula is A1+A2+A3. Assuming A1 can be 1 to 5 and A2 same , A3 same, the long hand calc is for me to run a data table using variables in A1 and A2 the fixing A3 (as 1)..note maximum result....then run data table again using variables in A1 and A2 and changing fixed value in A3 to the number 2...and so on and so on....in this simple example I know the max result would be 15, but much more difficult in my spreadsheet test.