I'm trying to recall the last time I tried to book in multiple parks. I think we did it on our October trip but not 100% certain. I know I did it on our August trip, without any problems.
@babydoll65 what message(s) did you get when you tried to book the additional FP?
I'm not surprised Guest Relations was unable to shed any light on it. They are probably totally unaware that it is even possible to do in the first place. That's one of those things that it's not even worth going to ask for help on.