# Perils of adding squared terms to model DOE data

I'm trying to model 3 level DOE data using 4 factors. Each factor when compared to the other factors looks like:

Since I have a center point and 3 points in a row for each factor, I think I can use 2-factor interaction terms in my model. But could I also use squared terms if I see curvature in either the leverage plots or the predicted-vs-actual plot as long as the VIF's stay low? When I do add these terms, they often come out as significant and improve the R^2 adjusted of the model, but I am worried this is just overfitting. If adding squared terms to these models isn't valid, what diagnostics could I use to convince myself?

What about for data which looks like this?: