I found this question here regarding a situation similar to my question except that this guy is getting married. In one of the answers EU Treaty article 39 is mentioned saying that he can also live in the EU if he is actively living with someone from the EU who has a job.
My case, I work for US companies remotely and my girlfriend lives in Romania. I always have to leave before 90 days and come back to the US for another 90 days in order to avoid overstaying the US 90/180 day limit for the EU. I would like to be able to stay with her as long as I want but it is not likely that we will marry anytime soon. While I am there, we live together though.
So my question is, what documentation or other methods are required to prove that we live together while I am in Romania so that I can be granted residency or whatever permissions I need to be able to stay?
I would have asked in the comments but I do not have enough rep to do so.