Is it really possible to be in a "closed" gay relationship?

well i have only been in one maleXmale relationship but that was an open relationship on his part, he was dating me and another guy (only one) and his other boyfreind told me that him and our boyfriend had done stuff with other guys and then a few weeks later my boyfreind asked me to try and date someone else AND him because he wanted to have a 4 some i think..... i told him **** no but anyways...... i do beleive you can have a closed relationship if the guy truly loves YOU