No.
... What? Do I have to explain? .. Ah fine, I shall do so.
It won't end well. Not once did I ever hear a couple say "Oh yea we had multiple sex partners, and it helped us realize how much we loved each other!" ... Not. Even. Once. Do you want to hear what happens to people like that? Either both people begin to question why they got together, one of them starts getting sexually addicted and makes the other person jealous of being that sex crazed, ooooorrrrrrr .... one of the swingers ends up falling for you or your girlfriend and vice versa. Meaning, one of the partners ends up replacing you or your girlfriend because of the investment. Trust me mate, it doesn't work.
I'm not saying you have to listen and refuse, but just know where i'm coming from. Sounds to me like you guys are both hesitant on the subject and there's a lot of concerns. Well, the reason is because this whole open relationship idea sounds awful and it's going to end up hurting you or her, probably you buddy.
If the relationship you currently have isn't working out, there are other much healthier ways in trying to make it work. If all else fails, this girl isn't right for you ... it's terrible to say, but you're much better off saving yourself from a world of hurt then going with this idea and then it slowly descends into whatever I listed above, the worst being your girl falls for one of her partners or you replacing your girlfriend with another girl during the 'swing'.
Alright is that enough? If not, let me know so we can talk. I'll be here for ya.