If you want to go one level deeper with that, would it be grammatically correct to say:
"We're arguing about whether we're arguing about whether we're arguing or not or not"
Or another level:
"We're arguing about whether we're arguing about whether we're arguing about whether we're arguing or not or not or not"
"We're arguing about whether we're arguing about whether we're arguing or not or not"
Or another level:
"We're arguing about whether we're arguing about whether we're arguing about whether we're arguing or not or not or not"