Can I add a player to two teams?

I have a small issue in my plugin. The issue is invisible players can be seen with their nametags.. I fixed this by doing:

Code:

addred.setNameTagVisibility(NameTagVisibility.HIDE_FOR_OTHER_TEAMS);
addblue.setNameTagVisibility(NameTagVisibility.HIDE_FOR_OTHER_TEAMS);

I was wondering if I could keep them on their team and make another team just for the invisible players and make it so they can kill each other such as this piece of code:

Code:

addred.setAllowFriendlyFire(false);
addblue.setAllowFriendlyFire(false);

But I was thinking how would the team see friendly Invisibles.
I'm currently using this method to have their teammates seen if their invisible:

Code:

addred.setCanSeeFriendlyInvisibles(true);
addblue.setCanSeeFriendlyInvisibles(true);

I want to do this: Make a team for invisible players and make them able to be on two teams so like blue/red and I want to make it so blue/red can see their teammates if they're invisible the teammates will be shown as a ghost like player how it is right now in 1.8. Please help.

 

In short, you can't. Minecraft only supports one team/player.

 

@Gorbit99 Thanks sadly I cannot fix this then