Originally Posted by bleego
3) That is polygamy. Polyamory is a bit more open on who is seeing who and what the extent of their relationship is. I know a few couple's who are married and have their boyfriends and girlfriends.
Polygamy simply means having multiple spouses. Polygyny is the term for many wives and polyandry means many husbands. If there is love involved in any of these types of marriages then they are polyamorous relationships.
Some couples approach poly by "adding someone to their relationship" and making some sort of a closed triad. Most often (though not always) couples seek to add another woman. This a pretty common way that couples who are new to poly approach it. While it often appears to be the safest way to approach polyamory, it tends to be the most difficult because the relationship is prescriptive. Meaning that you have a very specific set of requirements for what that relationship will look like (she will fall in love with both of us, etc) before the other person is even involved. This tends to constrict the other person. The most successful closed triads I know came together without planning it.
Other couples approach poly by just exploring relationships outside of the bond that exists between the two. These things work best when everybody is comfortable with everybody. But this often gives each member of the couple their own space to explore while still keeping the core of their relationship strong.
By the wording you used ("add another girl to our relationship") it sounds like he's looking for the former approach. If he's getting jealous over something like flirting, it definitely sounds like there's some work to do before approaching another relationship.