Almost all the cruise lines, except the luxury lines offer great pricing for the third and fourth person in the room. What varies more often than not is the category of room available to 4 passengers.
Carnival , Royal Carribean and NCL have a wide selection of 4 passenger cabins. Princess, Hal, and Celebrity are not far behind. But some ships have better 4 passenger cabins than others. For example, on the Celebrity Mercury 4 passenger cabins are only available on inside cabins, the lowest level of outside cabins, and then aft Verandas. The Mercury doesn’t offer any side veranda cabins with accomodations for 4 unless your book a suite.
The Celebrity Infinity offers 4 passenger cabins in almost all classes. When we sailed that ship three years ago, we had booked higher level ocean view cabin, and got upgraded to a 4 person veranda room. That ship could have also accomodated 4 in ocean views, family verandas, suites and even other cabins.
The old Rennisance crusie line ships are now owned by Princess and Azamara. On those ships the only 4 person cabins are small insides or suites. Some of the luxury lines like Crystal only offer triple accomodations.
Costa even offers free kids fares sometimes when they are 3rd and 4th person.
Probably your best bet is to find a date and an region your like and then shop around for the best deal on the total cruise. We were comparing two similar Trans Atlantics on Celebrity and Royal Caribbean. Celebrity had lower pricing on the1st and 2nd, but higher on the 3rd and 4th, but the overall cruise price was actually identical on the two cruise lines for 4 people.