It is possible to book a cabin with a third passenger (e.g. baby) although it's a cabin for two. But you need to request that via your TA or directly with MSC. They have a form for that, I can only give you the link to the german version, but this will be available in other languages, too. Normally the request will be approved (as long as there is lifeboat-capacity).
Officially the third person has to sleep in the parent´s bed, but they will will provide a cot in the cabin.
https://www.mscbook.com/pages/sdl/img/MSC_CRUISES_UEBERBELEGUNG_41816.pdf