Current Vagary campaign (http://www.playonline.com/pcd/topics/ff11us/detail/14205/detail.html) indicates you'll get 'an additional reward' when you turn in the five KI's. I turned in mine, picked the random 'whatever the master deems' option, and wound up getting two different random items (codex of etchings and plovid flesh, woo). Not sure if picking one of the other two options (to get a specific equipment or material) would give you a second pick of the same category, or if you get the chosen item and a second random drop. (I assume it just gives you a second, random drop on top of whatever you pick, regardless of category)