Yes, there will be probably be a formal night, usually preceded by beverages and crew members in the atrium and more photographers than usual. Dressing formally is optional -- many guests will, some won't.
You will be assigned to each dining room at least twice, and one 3 times, with a different menu each time. Each will serve a signature menu once. Depending on the cruise, you could then get a second menu for each restaurant, or all restaurants could have the same menu on the additional nights.
There will still be only 3 "main" theater shows, but there will be something happening in the main theater on most or all of the other nights -- this could include movies, singers, magicians, and/or comedians.
Palo brunch (and Remy brunch on the Dream/Fantasy) will available on each sea day, and the adult restaurants will have dinner seatings each night. Remy will also have a dessert experience in the afternoon on sea days. (Pro tip: Don't do brunch and desserts on the same day if you can avoid it.)
Sea days typically have more happening onboard than port days -- family crafts and game shows, presentations geared more to adults, lots of trivia, and lots of character meets. The shops will be open all day.
Happy planning!
