I'm not sure what you mean by the "bases." Are you talking about the carcases for wall and base cabinets? So I'm not sure what your question is.

My only concern would be that the prior refacing is sound and well-adhered to the face frames.

The book below has a good treatise on the subject.

Here is a link that might be useful: book on subject

Yes, I'm concerned about the face frames that are already covered in one layer of refacing. Was wondering if they just get covered over with another layer or if the first layer has to come off. It just seems like a second layer would make for a very thick cabinet. They do seem sound. I believe it was done professionally, so well that I didn't realize at first that they had been refaced.

This is not something I would tackle myself, but just trying to educate myself before I call a contractor who might promise results that can't be achieved.

Thank you for the link.