Elevator cabs are transferred between elevators, which may be shuttles, in various levels of a building, such as transport floors, in response to car calls registered in the cabs and hall calls registered on the transport floors. The cabs may be transferred from carriages or bogeys onto elevator car frames in a lateral direction, which is perpendicular to the motion of the cab on a carriage or bogey, or in a longitudinal direction which is the same as the direction of motion of a cab on a carriage or bogey. The horizontal/vertical control and transfer may be effected in response to the arrival at transport floors of elevators having cabs therein, or in response to the arrival at an elevator of a bogey carrying a cab which must be transported between a transport floor on one level of a building and a transport floor on another level of a building, in order to serve the need of a car call registered therein or a hall call. The horizontal transportation may occur on transport floors within a building, or may extend between different building segments or between different buildings.