I'm not sure I understand this concept. In $2^k$ designs, the independent variables have only two values and are coded as either being -1 (low value) or +1 (high value).
We can add a center point to the model (where the independent variables equal 0) but what on earth does this mean?
Is this some sort of data manipulation technique, so that we're adding fake data points to the model with plausible values?
Or are be actually adding new observations with intermediate factor levels to the model? If so, how is this still a $2^k$-model?