My girlfriend want me to have another girlfriend so we could have a three way relationship. Need help.

Hey everyone, hope you all are having an awesome day. I have a question for you all, something that I'm very much confused and uncertain about. But I need to give you the back story before i pose my question.

So my girlfriend was curious about men who have 2 or 3 wives in Muslim and other cultures. I'm from a Muslim household; so I was able to explain to her that under certain conditions Muslim men were allowed to have a second wife or third wife. But the conditions are very precise and I told her about all the conditions. After explaining it to her, she asked me if I wanted to have a second girlfriend. This was totally unexpected for me. And so I told her no and that I've never even thought of something like it.

At first, I thought that she was just asking me this as some kind of joke but she kept talking about it and she seem to be genuinely interested in trying a three way relationship. So I asked her how would this hypothetical relationship function.  The way she explained it is as follows: I am to take girl of my liking on a few dates. Then introduce them both. If she likes her then the three way relationship begins. If she doesn't then I look for another girl to date. Once we have found a third then I will have to treat both girls the same way. And she would treat me and the girl the same way. However, she does not want to be sexually involved with that girl, only emotionally and as a friend; but I would be allowed to have a sexual relationship with both.

I do not know what to do about this. Personally I would be interested in trying it but I don't know the ramifications. If this would be a good idea or a bad one? How would it effect my relationship my girlfriend?

Let me know what you think about all of this.

Thank you.