It sounds like on your turn you can use all the specials you want before a base scores.
But the instructions say if more than one player wants to it goes clockwise etc and it sounds like you each only get 1 special ability to use per turn and then it continues and you can use a another when play is back to you, until all players pass.
So on your turn can you only use one special ability say the pirate king, then if I have another pirate king(not even sure if there is two, just an example) I have to wait till play is back to me to move the next one.
Pretty much the only rule I can't figure out atm.
Twice you mentioned "on your turn" in conjunction with playing special ability cards, so I just wanted to be sure you know that the rules state that when a base is ready to score you can play special ability cards that happen "before" the base scores. In other words, it doesn't have to be your official turn. If more than one player want to play specials at the time a base scores they do take turns and go in "turn order," so perhaps that's what you meant.
So, to answer your question you do get to play all the specials you want, just not all at once if other players are doing the same thing. In fact, if no one else is playing a special card when a base has reached its "break point" and is about to be scored, you still need to resolve each of your cards one at a time, since some special cards allow you to play extra cards that have to be played immediately after the card is played or not at all.
I hope this helped!