The word 'more shut' implies that something is already closed, and needs to be closed further. So, if we are considering its antonyms, we would require words that give an entirely opposite meaning. Some of the antonyms for 'more shut' could be 'open,' 'ajar,' or 'unlocked.' These words provide the opposite of what 'more shut' means, i.e., something that is open or partially closed. However, depending on the context, the antonyms could differ. For instance, if we are considering a door or a window, 'open' or 'ajar' would be appropriate antonyms. On the other hand, if we are considering a container, 'unlocked' might be the more suitable antonym.