Not like titles or categories really matter for this conversation but I would say your bouncing on the line between an open relationship and a poly relationship.
To me it sounds like your really in the danger zone with your relationship. If your relationship is the most important thing do yourself a favor and cut the other guy loose asap. no contact. Normally I would never say that. But I also do NOT recommend Poly, Open, swinging etc to fix a current relationship. Your getting emotionally involved partly because you want to. You need to take ownership of that. Partly because there is a void, partly because of other reasons like the newness of it, etc.
In the 12 years I have been swinging I have seen many a poly relationship fail. Love triangles are not easy to handle. In fact never have I seen one succeed. But again finding myself slightly off topic.
I think you should date multiple men for the fun of the quart-ship and sex. It really needs to be enough people that you do not think about any of them in a way that threatens your relationship until you get a hold of those feelings and how better to compartmentalize them.