In the class settings you can choose the maximum baggage weight that's allowed in the class.
Also you can write it in the fare notification and it will appear to the customer during the booking process.
In the website you probably tried to add ancillary, in that case if you have an ancillary that is not limited to class/route it will show to all reservations. you can limit each ancillary to specific classes and not assign one to S class and it will not show when booking for S class.
And yes, it's possible to have more then 1 luggage for one person in a reservation (and of course multiple luggage in a booking)