I agree that it's somewhat confusingly worded, but have some Copypasta from the item forum:

I'm fairly sure that's not correct. They probably mean that you can re-write the augmented stats and replace them as many times as you want.

Here is the system as they're describing it:
1) You synergize some kind of augment for some kind of armor, which is capable of replacing any current augments on the armor.
2) You're given a dialogue that says, "Would you rather have this augment than the current one?"
3) You choose yes or no, and either implement the new augment or not.
4) If you don't like any of your augments, you're capable of removing them so you can store the piece with the porter moogles again.