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Cunard have weekly transatlantic sailings to and from New York, so you could obviously use these.
Many cruise lines have ships in Europe for the summer which return in the autumn to be used in the Caribbean. If you wanted more time in the States, these are an excellent way of travelling across the pond without flying. Ships typically cruise eastbound from March to May, and Westbound from September to December.
I think you'd need to do an awful lot of research and I doubt you's find them in both directions with the same company. You might manage to pick up a leg of a round the worls cruise for one section. The main problem will be that all the main cruise lines reposition in the same direction at the same time ie Spring early summer USA/Sth America to Mediterranean then Oct/Nov Med to Caribean. you migt be able to go med to caribean/Florida then pick up a reposioning cruise thro Panama canal to West coast USA or even fly across the states and get a cruise up west coast to Alaska, then fly back. It's a lovely idea th.