My thinking on this question is that a quadcopter is a subset of all multirotor drones. And if we have one subset of all multirotors, we may benefit from having the most common types such as hex-, octo-, tri-, and heli-.
Seems reasonable. Even though for many people these are functionally the same, on a fundamental level they're very different. The addition of rotors changes the dynamics and permits regimes of flight which are simply not possible with drones with fewer rotors.
multirotors tags could be joined by
octo-. Those would be optional, and would only make sense when the question is specific to that architecture. For instance, asking how many motors a multirotor can lose and still maintain full 3-D control isn't sensible if you have 4 motors or fewer.