Parking facility for motor vehicles, comprising: - a parking rack having two or more parking grids arranged side by side and a plurality of parking levels arranged one above the other, wherein the parking levels comprise an uppermost parking level, a lowermost parking level and at least one intermediate level interposed therebetween, and wherein at least one parking level (26, 28, 30) is connected or connectable to an entrance, wherein the parking rack defines parking spaces for the motor vehicles at intersections of the parking grids with the parking levels (26, 28, 30) and wherein the parking rack has at least one empty space in the at least one intermediate level; - receiving devices for the motor vehicles, which receiving devices are positionable in the parking spaces; - at least one displacement device operative at a respective parking space for displacing the receiving devices in a respective parking level (26, 28, 30); - at least one lifting device having lifting elements, wherein at least one lifting element is arranged at a respective parking grid, which lifting element is selectively coupleable to one of the receiving devices for the vertical transport thereof within the parking grid; - a control device for controlling the at least one displacement device and the at least one lifting device; wherein: - the receiving devices in at least the at least one intermediate level are configured to assume, by control of the at least one displacement device by the control device, in the respective parking grid, a transport position in which they couple to the at least one lifting element for vertical transport; - and to assume at least one pass position in which, by way of the at least one displacement device, they are, relative to the transport position, displaced laterally within the parking grid such that the at least one lifting element is vertically movable in the respective parking grid by way of the at least one lifting device and thereby passes past the respective receiving device; wherein: at least one support device, in particular several support devices, is/are provided for supporting the receiving devices when these are arranged at the parking space, and the receiving device is supported on the at least one support device, wherein at least one support device is arranged at a respective parking space; characterized in that the at least one support device in at least the at least one intermediate level is transferrable from a supporting position in which the at least one support device supports the receiving device in the parking space, to a release position, and vice versa, in which release position the parking grid is released for vertical transport of the receiving devices (38, 104) by way of the at least one lifting device, past the support device. - a parking rack having two or more parking grids arranged side by side and a plurality of parking levels arranged one above the other, wherein the parking levels comprise an uppermost parking level, a lowermost parking level and at least one intermediate level interposed therebetween, and wherein at least one parking level (26, 28, 30) is connected or connectable to an entrance, wherein the parking rack defines parking spaces for the motor vehicles at intersections of the parking grids with the parking levels (26, 28, 30) and wherein the parking rack has at least one empty space in the at least one intermediate level; - receiving devices for the motor vehicles, which receiving devices are positionable in the parking spaces; - at least one displacement device operative at a respective parking space for displacing the receiving devices in a respective parking level (26, 28, 30); - at least one lifting device having lifting elements, wherein at least one lifting element is arranged at a respective parking grid, which lifting element is selectively coupleable to one of the receiving devices for the vertical transport thereof within the parking grid; - a control device for controlling the at least one displacement device and the at least one lifting device; - the receiving devices in at least the at least one intermediate level are configured to assume, by control of the at least one displacement device by the control device, in the respective parking grid, a transport position in which they couple to the at least one lifting element for vertical transport; - and to assume at least one pass position in which, by way of the at least one displacement device, they are, relative to the transport position, displaced laterally within the parking grid such that the at least one lifting element is vertically movable in the respective parking grid by way of the at least one lifting device and thereby passes past the respective receiving device; at least one support device, in particular several support devices, is/are provided for supporting the receiving devices when these are arranged at the parking space, and the receiving device is supported on the at least one support device, wherein at least one support device is arranged at a respective parking space; characterized in that the at least one support device in at least the at least one intermediate level is transferrable from a supporting position in which the at least one support device supports the receiving device in the parking space, to a release position, and vice versa, in which release position the parking grid is released for vertical transport of the receiving devices (38, 104) by way of the at least one lifting device, past the support device.