Novel physics and reversal mechanisms of the whole system switching (WS) and individual switching (IS) type are reported for hard/soft TbFeCo/YFeCo exchange-spring multilayers. The WS type usually occurs in multilayered systems, in which the magnetic anisotropy of hard TbFeCo layers is neglectable. For such a system, the ferrimagnetically coupled hard/soft multilayered state is recovered after removing applied fields from the magnetized state. At low negative fields, the magnetization switching occurs collectively for all magnetic moments in the whole system. In this case, the low-coercivity mechanism is discussed on the basis of a hard/soft interfacial point contact. This configuration is realized for TbFeCo/YFeCo discontinuous exchange-spring multilayers, in which the magnetic (Fe,Co) nanograins coexist with non-magnetic amorphous phase in the soft layers. In this state, a magnetic coercivity as small as 0.4 mT is achieved. It is considered as an excellent magnetic softness of rare-earth-based systems. Enhancing the magnetic anisotropy in the hard TbFeCo layers, the magnetization switching follows the IS type at low temperatures. Starting to decrease the applied magnetic field from the high-field state, one observes the first reversal of the magnetic moments in the soft high-magnetization YFeCo-layers in positive magnetic fields. This is the reason for the observation of the negative coercivity as well as negative-biasing phenomena.