The word "brain-case" refers to the part of a skull that contains the brain. This term is commonly used in anatomical and scientific discussions, but there are some synonyms that you can use to add variety to your language. One alternative term is "cranium," which is the bony structure that protects the brain and provides attachment points for various muscles. Another possible synonym is "skull," which is the entire bone structure of the head. Additionally, some people might use the term "neurocranium" to refer specifically to the part of the skull that protects the brain. By using these synonyms appropriately, you can make your language more rich and precise without sacrificing clarity or accuracy.