Facebook and Game Center Conflict

[>[Droopy]<]

I was wondering if there is a way to link a new Facebook to my account through Game Center on my iPhone. The Facebook that is currently linked to it has an unwanted game save for Narcos: Cartel Wars and when I link a new Facebook to it it keeps the game save that is on the other Facebook. I have opened and closed a number of Facebooks in an attempt to link the game on my iPhone to a Facebook with the same save info. Somehow they all get polluted with the save I do not wish to keep that was on my old Facebook. Is there a way to fix this? If not am I in danger of losing my progress if I just use my Game Center information? Any input would be appreciated.