For clarity, my passport was stamped on arrival and departure at FDF airport, even though we were flying to France. It was not stamped at the cruise terminal.
It's definitely possible to get on at different ports with MSC because quite a few people did it on our cruise. Even though FDF was the last stop for everyone people boarded at pretty much every port along the way.
What I don't know is if this is only allowed for EU passport holders.