There are actually several Offensive Influence sets with the same name and effects. Items from a different set will not contribute towards the set bonus in another set. In other words, you will not get a two set bonus for just wearing both a Crusading Bangle and Onslaught Mantle, since they belong in different sets.
EQ2i credits this article at Census for the info in this article. the last update on Census for this item was: Tue, 18 Sep 2018 15:00:34 +0000