What does the third level refer to?
The Grand Central Station of New York has subways on two levels from where the commuters take trains to different destinations. No third level was ever built. However, the protagonist of the story, Charley, believes in the existence of a third level, operating in a time-frame of 1890s.
The third level signifies an escape from the modern world that is “full of insecurity, fear, war, worry and all the rest of it....” The period of 1890s represents a peaceful life not possible in the present era. From this level, the protagonist wants to travel to Galesburg, Illinois, with his wife Louisa. For him, it is a part of reality while his psychiatrist friend calls it a “waking-dream wish fulfilment.”