Can you stain would that has primer on already?

Yes, you can stain wood that has primer on it, but the results may not be ideal. The primer creates a barrier that can prevent the stain from penetrating the wood evenly, leading to a blotchy appearance. To achieve better results, it's recommended to sand the primed surface lightly to promote adhesion, or to use a specific stain designed for use over primer. However, for the best finish, it's usually best to stain raw, untreated wood.