Really feel for you Op. I've been in this exact situation and unfortunately it didn't end well.

In my case, the person used polyamory to justify cheating amongst other things. Cheating being messaging others, claiming to be single, in hopes of sleeping with them.

Please sit down together, go over your wants and needs. Be honest with how things make you feel, and really try to listen to their feelings too.

If you do decide to try polyamory, be specific about what's expected and any boundaries. Define what you consider cheating. There's many configurations with polyamory and it's not one size fit all.

If both your wants/needs are incompatible, don't compromise your happiness for that love. As much as it sucks, love isn't worth hurting that person or being hurt by them.