Are you sure you want to know?It is grammatically correct, but I can't imagine anyone saying this. What else might you be expected to do with a pizza?
I'd be more likely to include "a" in BrE, just like we go out for a beer. Although, I probably wouldn't go out and eat three or four pizzas in a single session.We would commonly drop the article and simply say "and go out for pizza..." But I might say "meeting up" rather than just "meeting."
I think I agree. When you meet up you've already "gone out" (unless you meet up at your or your friend's house)."Meeting" followed by "go out" sounds wrong to me.