From the Wikipedia article on Linda Ramone:
Relationship with the Ramones
Linda originally dated Joey Ramone but later dated and married Johnny Ramone. Stories conflict whether Joey and Linda had broken up prior to Linda dating Johnny or if Linda left Joey for Johnny.
Why had broken up should be "whether Linda and Joey broke up before she dated with Johnny"? In this sentence what comes first the dating then the breaking up that is the problem, I think! I have found the answer to my question: past perfect is used as something that had not arrived yet but was going to happen.