overriding this java method, how can I add a new item to the map?

override fun extractAuthentication(map: MutableMap<String, *>)

e.g. when I want to add a list the compiler says: “Required Any? found List<String>”

MutableMap<String, *>

means: A map with string values and I don't know what the values are. If you don't know what the values are, you cannot safely put anything in, because you cannot know if it would fit.

But I cannot declare/overwrite it differently, can I?

No, you can't, but you cannot safely put stuff into this map

@frogger probably needs a MutableMap<String, Any?> not a MutableMap<String, *> The former implies you can add anything, the latter implies you can only add the one type we don't know (and thus you can't add anything)