Jim, passenger capacity varied according to the whims of the inspectors. When the America came out in 1918 she was a "half-boat" with staterooms half the length of the cabin and a dance floor the rest of the way. This compromise did not last and the staterooms were later removed. She started out with 3,600 and was later increased to 4,000. Still later she was reduced to 3,600.
As a sidelight, when I was in the Belle of Louisville's crew she was allowed 1,353 passengers and crew. On one occasion we carried more than 1,600 - this with the entire USCG contingent aboard! Today the boat is still allowed about 1,200 but the management chooses to restrict her to 800. At about 600 passewngers problems arise about tables. At about 900 seating becomes a problem. Above 1,000 everything goes wrong.
As a result of that experience, I would say the America occasionally carried more than 4,000. No manager wants to turn away customers.