Hi,
There are other examples;
Low voltage UPS.
You can have a synchronous buck batter charger, working as a synchronous boost in the back-up mode.
This is two quadrant positive voltage, positive and negative current.
TEC controller
This is two quadrant, positive voltage, positive current and negative voltage, negative current.
A class D amplifier is four quadrant.
A 4 quadrant power supply must be fed by a two quadrant power supply, that is one that can absorb power.
In two of the quadrants power is flowing from the load back to the source.
Regards,
Jay_Diddy_B