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The rules do not seem clear on this. Can multiple railroads start from the same city hex? So could Memphis (for example) be the eastern terminus to four (or more) railroads?
Each railroad may have only one cube in a hex.
No more than three railroads may occupy a single hex.
A railroad may occupy no more than one single starting city hex.
A railroad may only occupy a single Port City.
Port Cities may only hold one railroad.
These are the only restrictions on how many cubes may be placed in a given hex. Any other placements that follow the placement rules are legal.
So, yes, up to three railroads may start from the same starting city hex.