SpaceX Moon
SpaceX have no goal to go to the moon itself but is willing to support moon missions
The first private mission is a moon flyby with two paying passengers that was originally for a Falcon Heavy but now looking to be delayed for the BFR.
SpaceX have done mission design work for a posible moon base
Moonbase Alpha with 3 BFS showen landed
nice graphics for a SpaceX BFR Moon Landing