Before the cruise, each passenger 18 and older can be booked in 1 of each type of experience at Palo (and at Remy or Enchante on the newer ships). As mentioned above, the first night at Palo is considered a different type that other dinners, so you can book 2 dinners if one is on the first night of the cruise.
Once you are onboard, you can inquire whether there is available space on additional nights. You can go to the area for dining changes on embarkation day, or stop by the Palo check-in desk later in the cruise.