A stable suspension of nanoscale particles due to the Casimir force is of great interest for many applications such as sensing, non-contract nano-machines. However, the suspension properties are difficult to change once the devices are fabricated. Vanadium dioxide (VO$_2$) is a phase change material, which undergoes a transition from a low-temperature insulating phase to a high-temperature metallic phase around a temperature of 340 K. In this work, we study Casimir forces between a nanoplate (gold or Teflon) and a layered structure containing a VO$_2$ film. It is found that stable Casimir suspensions of nanoplates can be realized in a liquid environment, and the equilibrium distances are determined, not only by the layer thicknesses but also by the matter phases of VO$_2$. Under proper designs, a switch from quantum trapping of the gold nanoplate (on state) to its release (off state) as a result of the metal-to-insulator transition of VO$_2$, is revealed. On the other hand, the quantum trapping and release of a Teflon nanoplate is found under the insulator-to-metal transition of VO$_2 $. Our findings offer the possibility of designing switchable devices for applications in micro-and nano-electromechanical systems.