You could probably have a situation where two countries each own their half of a metro area and come to an agreement where residents of the metro could cross very easily. For example if Greece owned European Constantinople and Turkey Asian Constantinople, residents of each half could get an ID allowing for visa-free movement to the other side.
That would essentially be a Constantinople-Scutari (Istanbul-Uskudar) situation. Scutari/Uskudar was separate from Constantinople until the early Turkish Republic era. By separating the Bosphorus between Greece and Turkey, you'd end up with separate identities, and eventually aside from the free movement, you could tell that Constantinople is Greek and Uskudar is Turkish.