Any way to change system volume?

I can't vouch for OS-specific plugins, but there's no way built into Unity, no.

You can manipulate the master audio listener's volume, though.

Typically applications can't access this. There is a reason you have a master volume. Its so the user has control over the volume regardless of what your application is doing. This sort of feature would quickly get abused by advertisers ect, to the point you would be begging the appropriate operating system owner to design it out.

Besides, how do you expect kids to play your game at school when they are supposed to be in class if you keep turning up the volume?