Threesomes are fun for sure but they create a sexual energy that is different than two alone. One has to consider everyones feelings and there is a sense of being outside looking in more often. Two people can get lost in each other and relax into that more. Both can be connecting and deep, but in differing ways.
Perhaps you are desiring closeness with this woman one on one? There is nothing wrong with that, but being honest about it is the best bet to success. Your fiance might find a threesome fun with her, but if you have deep feelings for this woman then they will deepen with sex and she will find herself feeling resentful about that perhaps.
In my experience, threesomes with people I am friends with and my husband have been the fun and playful. Threesomes with the two men I love have been fantastic and bonding, but threesomes with someone I know I want a deeper bond with and could love but there isn't space for that in our lives for whatever reason, have been a disaster and painful. Unfortunately I didn't fall for him until after a few times, so who's to know, but you are in a situation where you KNOW you could love this woman. That is different. I suggest you don't do it and work out being with her alone as a girlfriend, if she and your fiance are cool with that and willing to work on being metamours.
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