I have alternatives that a user can select from, and a toggle button to switch whether they work like a radio button (allowing exactly one alternative to be on at a time) or as toggle buttons (allowing them to work independently of one another). The interface is in English, and I would like a short English word to describe this behaviour of the button that switches this, especially the state of the alternatives working like radio buttons. What is the best word for this?
Maybe something mentioning groups (as in they are all part of the same group) or perhaps something more explicit to imply that they are mutually exclusive like "choose only one answer" or "single answer".
Reading your question again, I think "multiple answers" and "single answer" are a good way to go. Or maybe just "single" and "multiple" and perhaps changing the style of the buttons from radio to checkboxes could also help.
From what you write in your question it sounds like you are actually letting the user select between single choice and multiple choice. This control overrides what other choices the user have made already, which you need to handle. Do you reset already given selections (by the user) or do you allow them to be seen in a disabled state? To me this is more important than the word of the button.
If you want only one word, I would say that it is a switch, like a main switch. If the switch is off, it's radio button functionality - and if it's on, it's the multiple choice functionality enabled. Therefore I would call the button a "Multifunction Switch". But if you need one word, I'd pick switch or selector. But that doesn't tell the user what the switch does... So I'd use two words instead. And since its behavior works as a main switch it would be larger in size and bigger font.