Off the top of my head, there was a rift (to say the least) between the Lucchese Family and its NJ crew in the late 1980s. This rift led to Accetturo turning state witness after the Lucchese bosses (Amuso and Casso) ordered killings on several leading members of Accetturo´s crew (Accetturo included).
This was when Amuso gave the infamous "whack Jersey" order to take out the whole northern NJ faction of the family who were refusing to give a bigger percentage of their profits over to NY.
