For real life examples, search for "Kieferorthopäde" (that is, orthodontist) and "Dr. Dr." or for "Kieferorthopäde" and "DDr.". In Germany and Austria, orthodontists typically study both medicine and dentistry, and some of them do a doctorate in both disciplines. Germans seem to prefer "Dr. Dr.", whereas "DDr" occurs primarily in Austria.
The usual form in Austria would be "DDr.", which you see quite often, especially on lawyer's plates. After that, it would be DDDr. (and probably so on).
Remark : He is at least DDDDDDr.: https://www.nachrichten.at/oberoesterreich/Das-ist-Doktor-Doktor-Doktor-Doktor-Doktor-Doktor-Norbert-Heinel;art4,843952
(Other countries may have other customs, but this has been my experience)
In most circumstances, no one bothers writing "Dr." as a prefix anyway! Informal situations in general tend to drop prefixes and suffixes, especially honorifics and degrees. I guarantee you that Paul McCartney doesn't make dinner reservations as "Sir Paul McCartney". Most people with ...