If you continue you're behavior and he continues to play you, the girlfriend will find out and you will probably start seeing him. Warning' "What goes round, comes round".

I think they are both playing a game.

Hi Op just a quick word, I think the term you may have meant is Polygamy.

I think she used the right word, in the right context. Although I admit to never having heard the term before, there is a definition for it here.

Polyamory - Definition and More from the Free Merriam-Webster Dictionary

Polygamy, is more to do with being married to two or more partners at the same time.

Polygamy can be defined as any "form of marriage in which a person [has] more than one spouse at the same time."

En.wikipedia.org/wiki/Polygamy

Thanks Jake I stand corrected, thank you for the clarification. Pp