The Cambridge Dictionary offers this meaning of span:
If a bridge spans a river, it goes from one side to the other:
The verb span means to go directly from one point to another: if a bridge is made up of multiple segments, each going from one pillar to the next, each segment is called a span, and the bridge as a whole is called a multi-span bridge.
A door that is installed correctly can only ever span a doorway- going from one doorpost to the other doorpost. If the doorposts are close to the edges of one side of a room, you could say that the door spans that side of the room, but if you have multiple doors on one side, then each door only spans one doorway.
If you want to describe a room where every wall has multiple doors, you could use the word line, which means
to form a row along the side of something
Note that this relates to only one side, so you would have to say
Doors line every side of the room.