I believe "on" and "off" in electronics typically correspond to different voltage levels. So you absolutely could have a third intermediate state if you wanted to. Flash memory does this (and even sometimes has 4 states). I guess designing switches (transistors) that could take advantage of and propagate these extra states could be tricky though.
Binary for electronics is obvious because there are 2 states in electric components: on or off. There is no 3rd option.