When Museum was originally kickstarted, the solo mode was included as an exclusive. Unfortunately, it only allows the player to use it with the base game (according to comment by Holy Grail Games). None of the expansions is solo-compatible which is a shame, as several have been and will be published.
In any case, in the solo game you are competing against rival curator Alphonse Legros. Your goal is to amass a great collection of artifacts from all over the world, and at the same time deal with historical events and the scrutiny of the public opinion. Presumably for the shady ways in which you acquire your treasures.
This campaign offers: A deluxe box with Game Trayz. An update pack of the rules of the base game. Two new expansions: The Historians, and Cthulhu Relics. Plus, all the Kickstarter exclusives of the first edition, among which is the solo mode. So, if you interested, you may purchase the base game from the stores and then wait until the delivery of this Kickstarter to play it.