I've been reading some Latin of the 17th and 18th centuries and am wondering if it is possible for there to be "double diminutives." As I understand it, the word "cerebellum" (Oxford Latin = "brain") is a diminutive of "cerebrum" (also "brain"). But I've found an 18th-century author who coins the term "cerebellula." I know that "-ula" is another diminutive ending, so I'm wondering if it really might be the case that "cerebellula" is a double diminutive, meaning "little little brain" or "tiny brain."
Is this possible, and is there any classic/medieval/Renaissance Latin precedent for this move?