Actually it's done everyday right under many Titanic Enthusiast's noses. Take the CNN video clip that is posted on this group's movie clip page http://www.titanic.com/modules/mydownloads/
That ship is not the Titanic. When that is shown moving surrounded by tugboats is actually the Olympic. If you notice the stern of the tugboats, the names of the tugboats are scratched of each frame of the original film cells by hand which makes that area look like fire or material waving in the wind. This was done so that the tugboats could not be traced to the Olympic and the identity of the ship could be changed to a Titanic imposter. I have many collections of old archival footage that have the names of the surrounding ships and boats obscured. Even some footage of Captian Smith on board the Olympic was altered to obsure a ship's name that is docked next it and then refered to as the Titanic. Many aren't aware that on her maiden voyage, Captain Edward J. Smith, was captian from Southampton to New York via Cherbourg and Queenstown on June 11 took 5 days and 16 hours. That September Olympic collided with HMS Hawke in the Solent when her triple screws caused such massive suction that the cruiser was pulled into the larger ship's stern. Olympic was held to blame, and after repairs at Belfast resumed service on November 30. Following the loss of her sister ship Titanic (then under Olympic's erstwhile Captain Smith), Olympic underwent a massive "safety-first" rebuild including the installation of an inner skin and the installation of enough lifeboats to accommodate all passengers and crew.
Although very closely matching, there were differences between the Olympic and Titanic. The promenade deck on the Olympic, for example, was fully open while the Titanic was fitted with windowed covers over 1/3 of the length of the promenade deck. The Titanic also had some extra luxurious suites on the B deck that the Olympic lacked.
Compare these photos I have of the two.
http://img.photobucket.com/albums/v607/sundancekid17/Titanic%20compared%20Olympic/compare.jpg
http://img.photobucket.com/albums/v607/sundancekid17/Titanic%20compared%20Olympic/compare2.jpg

Sundance