I've been dating this guy since the end of May. But we aren't in a relationship should I still date other men?

This guy and I have been on at least 10 dates (we started dating at the end of May). But we haven't said we were together. We just said we wanted to see how things progress between us. Recently he ran into one of his friends while we were out together. And he wanted me to meet him but I wasn't ready yet. And he just bought me a swimsuit to wear to the beach tomorrow. We haven't said we are actually in a relationship. He said he hasn't been dating anyone else and I haven't either. But there is another guy who wants to date me.

I don't want to date other men this is not what I'm implying. I'm asking if I should date other men since we aren't in a relationship.

Also, is a six-year age difference too much? I'm 37 and he's 31.

Updates
1 y
We've been sexually involved twice.
I've been dating this guy since the end of May. But we aren't in a relationship should I still date other men?
Post Opinion