Well, I know you said you don't know what terminology to use, but I am going to point out something in what you said, that seems to indicate a certain way of thinking that might set you up for disappointment.
Basically, it is this: You don't really "add" people to your existing relationship, like condiments to a meal. How would you feel if you were a woman who is "brought in" to "add to" someone else's relationship? Would that be appealing to you in any way? Likely not.
You develop relationships with individuals. It would benefit you, and anyone you might get involved with, to keep that in mind. If you meet someone you're attracted to and want to see where it goes, then you would engage in and invest your energies in a relationship with that person, and if it takes off, you would then simply be managing more than one relationship. What would you be adding, and adding to? The idea is silly.
You add ketchup to french fries, or sugar to coffee, to enhance the flavor - you don't add people to enhance an existing relationship. People aren't condiments or pickles for your sandwich. No one is put here on the planet to enhance the relationship you have with someone else. Everyone wants something that they can call their own, and each dyad should be able to stand on its own strengths and merits. If you want an additional relationship with someone else, leave behind the Couple-Plus-One mentality and forget about the notion that you'd be adding someone to your marriage. If you can remember that, you might have a shot.
Read this thread for some insight:
Added to, Joining In 
