To answer your initial question, Yes, it is possible, but in my relationship it is basically required that everyone treat everyone as equal and lovingly as possible and that all parties 'are primaries' and our relationship is closed otherwise.
To remark on the rest of your situation...two months is too soon, four months is too soon, six maybe. This coming summer I will be moving in with one of my partners as we are in an LDR, as she's the newest partner we'll have been partners for almost year and a half at that point and we'll have been close friends for about three years total (including my partners as the closest and most intimate kind of friend).
Jumping on it after only two months seems like a recipe for disaster. You will be at the mercy of the wind and their mood. His partner that it doesn't seem you know much about at all will (be in the same house?) have significant power over the stability of your living arrangements.
Not only would I advise heavily against rushing this, I believe you need to visit often for a fair period of time, set up a place of your own in the area even if it causes more financial challenges, take your time to be careful. Visit them as often as you can, talk, come to agreements, be affectionate, but lay the grounds and get to know eachother well. Make sure you can live with him.
I know in some ways what I'm saying might come off as harsh and painful in it's slowness. But be slow and steady and in truth things will happen fast, haste will make waste and little will last.