A top notch rcm with appropriate fluids and care should not add more tics, pops or glaze on a cleaned record. It would seem that a subsequent cleaning with the same or, preferably, a different machine with different fluids will, if done properly, cause no harm---and probably help to clean a record a little better. I am still very happy with the Audio Desk rcm and I am cleaning many more records than I did with my VPI 17F which, btw, I think is a fine machine. As for my search for the ultimate record cleaning machine---I'm done.
PS- With thin records, there will sometimes be a few drops of water/ fluid left on the record which cann be blown out with compressed air. I believe this can be easily remedied with slightly bigger squeegee flaps which the manufacturer could easily supply. They slide in a space at the top of the rcm. Thus you could have more squeegee space for thick records and less for thin records.