I am sorry your SO will not even tolerate a conversation on the subject. She obviously feels very threatened.
It sounds like you are faced with a choice of living life by her rules ~ or not. It's not a question of whether her reaction is reasonable or fair, it's a matter of this is the reality.
I myself am newly out of a triad with a couple in which the wife went from fully encouraging the idea to full blown jealousy in which her husband was given an ultimatum ~ her or me. You know how that went. It was very painful for all of us.
With your SO not even able to discuss the topic, I don't see this boding well if you continue to push it.