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But remember that 5 in one cabin can be rather cramped and you do only have one bathroom...
If one child can go in a cot the answer is yes possibly - otherwise all lines i know of do not give details for a fifth person - so no. some companies do family suites though. call a cruise agent ie the number above - freephone 08000911629 !!!!!!!
Some of the newer Royal Caribbean Ships (Freedom, Liberty Independence, Oasis etc) do have family cabins which will accomodate 5 to 8 depending on which one you chose and they range from insides to outsides to suites.
Southampton : Alicante : Barcelona : Marseille : Florence/Pisa : Ajaccio (Corsica) : Gibraltar : Seville (Cadiz) : Southampton
Now from £813pp Was £1065pp
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Southampton : Barcelona : Corsica (Ajaccio) : Rome (Civitavecchia) : Florence/Pisa (Livorno) : Genoa : Marseille (Provence) : Gibraltar : Southampton
Now from £999pp Was £2019pp
Southampton : Bilbao : La Coruna (Spain) : Cherbourg (France) : Paris/Normandy (Le Havre) : Southampton
Now from £585pp