We've dined at Palo on the Fantasy as a group of 16 for dinner, but split into two tables of 8 next to each other.
As a group of 12, we've been seated in the "private" circular area for Palo dinner (where they lay the buffet tables during brunch). I think the maximum they will seat together is 12, as we were seated at one long table for brunch that trip.
Both times we weren't able to secure reservations until we got onboard.