I have seen 6. We usually have a relatively large group and take our time over dinner. The big drinkers in the group hit 6 at times. Once the waitstaff learns your preferences they often have one ready for you as you are sitting down and they keep them coming.
As far as cutting people off goes, have seen that multiple times. Sometimes a bartender will tell the person in question there is a time restriction to slow them down, sometimes they will ask them to slow down a little and give a water instead of a cocktail/beer. And sometimes they will flag their account, not sure if they have to call guest services or a manager to approve the flag, but it happens.