You might consider using a predictive model to explore the response surface. You might use a multiple linear regression model if the response is non-linear but with few modes. You could also use a Gaussian Process or Neural model. There are many more to try. You may use the Profiler with any JMP model to visualize the surface.
Have you validated the data to look for data errors or explored the data for outliers that might be correct data but could distort a model?