If you do this, you are running parts of the design in 2 blocks and therefore might (likely) need to account for the block effect.
I don't know anything about your situation, like the number of factors you are looking at, but typically if you are doing RSM, you already have data to support a first order model AND you have a good amount of information about noise. If not, perhaps you can do sequential experimentation and start with fractional factorials and block designs.
"All models are wrong, some are useful" G.E.P. Box