In German-speaking countries, or at least in Austria, the abbreviation
DDr. mult. is used to denote people who have more than two doctorates. Googling for
DDr. mult. allows one to identify some persons, but I cannot quickly verify whether they received just three or even four+ such titles.
However, note that some of them should actually be labelled
DDr. h.c. mult., whereby
h.c. (honoris causa) suggests that the doctorates are honorary titles. In other words, oftentimes they did not start PhD programs from the beginning to the final defense of their dissertation multiple times, but perhaps just once, whereafter they received some honorary titles for some public service.