Currently Wikidata is setup in a way that a user can only add labels in languages that the user knows according to his userpage.
There are many cases where a user who research a certain concept can find information about how the concept is called in various languages that he doesn't speak. Anatomical terms often have a Latin name that's easy to research even for users that don't speak Latin, but depending on the context it can also be possible for a user to know the translation of a term into more languages that he doesn't speak.

I think the box in which the current labels get edited, that the user can access by clicking on edit at the top of the page, should support that usecase. I therefore propose that a new "Add language"-button in a new line after the list of current labels.