My partner is pushing me for threesome

I (27M) have been in a relationship with my girlfriend (26F) for about a year now. Things have been great between us, and I genuinely thought we were on the same page about our relationship.

However, recently, she confessed that she has feelings for someone else but insists she doesn’t plan to settle down with him. Instead, she’s been pushing me to have a threesome with her and this guy. I told her I’m not comfortable with the idea, but she says it’s her dream to experience this at least once. When I said no, she brought up the idea of getting my "permission" to do it with some of her other friends instead, even if I don’t join.

I’m honestly confused and hurt. I care about her, but this isn’t something I ever saw coming. I don’t know how to handle this situation or where to draw the line. How do you deal with this kind of situation without damaging the relationship further? Any advice would be appreciated.