Royal Caribbean has the ultra spacious rooms, but they differ according to ship class. These have the king bed, pull out sofa and a set of bunk beds. The problem is figuring out which type they fall under. Some ships only have them as interior, some as ocean view, and some have this option with a balcony. And, they often book fairly quickly. So, you have to do a mock booking for a family of four, find a sailing with the ultra spacious room available and then call in to book it since you have more than four people.
Or, if you are able to splurge, there are a few 2 bedroom suites available. I have never been able to cough up the money for one of these rooms though.
Keep in mind, kids sail free promotions are not usually good for any sailings during school breaks. So, you may not be able to grab one of these promotions unless you homeschool or are willing to take the kids out of school during the trip.
We have done one of these ultra spacious rooms as an ocean view and loved the extra floor space it gave us. But, we have also done the connecting rooms and really appreciated having a second bathroom.