One of the issues others have not mentioned is the fact tha you are interested iin her relative/family member.
Even if she would agree to a non-monogamous relationship with you this does not mean she would be okay and fine with you having sex with with her relatives/family members/closest female friends.
That might be too close for comfort and also endanger her family relations/BFF relations if things don't work out. This could cause some nasty family drama, same with dating close friends.
So perhaps if she even agrees to a non monogamous relationship you should find your other partners outside of her family members/closest female friends circle. Perhaps someone she doesn't know or is a vague aqueintance.