One thing to clarify-you're not sharing the family-platter with other tables, your family is seated at their own table & they bring a platter that is just for your family.
And at the family-style meals, it is all you can eat...if you would like more, you just ask for more (either the whole platter, or you can ask for specific part you want more of.) For example, at The Garden Grille in May 2008, we really like the potatoes & the flank steak, as well as the corn bread so we asked for more of those. The waiter brought out more immediately (actually too much more! We were so stuffed we couldn't finish the de-lish dessert.)