Dubbed the Mafia Titanic Mod
it lets you "explore the meticulously recreated and highly populated ship with accurate interiors and lavishly detailed environments" of the infamous ship. This mod has been in development for a whopping 15 years, which explains why it's associated with the original Mafia
Even so this is Part One of the story, which doesn't include the eventual sinking. But there is a story involving the Salieri crew boarding the maiden voyage of the Titanic - and from there you can explore the entire ship, dine in the lavish dining area, swim, and more. In addition to the visual setting all of the sounds and atmosphere have been created to set the mood of being aboard the actual giant ship.
To install the mod you'll need a copy of the original game Mafia - City of Lost Heaven (2002) -- as available on Steam