Do you not, yourself, have any desire to have an OSO? Do you characterize yourself as somewhat shy or introverted, and thus the prospect of going out and meeting new people is somewhat frightening?
These are all things to work on. Maybe start out just by meeting people without any intent to hook up, date, or have anything more than a few hours of pleasant conversation. Maybe you never go farther than that. Maybe you make new friends. Maybe one or more of them blossoms into something more. If you self-identify as mono, nothing bars you from making new friends, at least.
Do you have any hobbies that your girlfriend doesn't share? If so, do them. Is there anything you've yearned to do that she doesn't? If so, do it.
Certainly, do not keep your feelings from her, or they'll only fester and you'll eventually start blowing up over seemingly unrelated small things. Trust me on this--I'm a champion at holding things in out of fear of my wife's reaction, and it just gets harder to bring stuff up the longer you avoid it. That said, learn how to discuss your emotions using non-accusatory language ("I" statements, open-ended questions, and so forth, instead of "you" statements--by doing so, you show that you're taking ownership of your own emotions instead of blaming her for them).
What do you gain? You gain a more contented, more relaxed girlfriend, who isn't looking for excuses to blow up your relationship (either consciously or unconsciously) in order to pursue a new love interest. This, in and of itself, is HUGE, and makes it more likely, rather than less likely, that your relationship can live out its natural course instead of coming to a premature end.
Having said *that*, do make sure to ask for what you want, and look after your own needs in the relationship.